Page 1 ( ) EXERCISE 16 A Q.1. Take three non-collinear points A, B and C on a page of your notebook. Join AB, BC and CA. What figure do you get ? Name : (i) the side opposite to C (ii) the angle opposite to the side BC (iii) the vertex opposite to the side CA (iv) the side opposite to the vertex B A C B Sol. A, B and C are three non-collinear points in a plane. AB, BC and CA are joined. A C B (i) The side opposite C is AB (ii) The angle opposite to the side BC is A (iii) The vertex opposite to the side CA is B (iv) The side opposite to the vertex B is CA Q.2. The measures of two angles of a triangle are 72º and 58º. Find the measure of the third angle. Sol. The measures of two angles of a triangle are 72º and 58º But measure of three angles of a triangle is 180º Third angle will be = 180 – (72º + 58º) = 180º – 130º = 50º Q. 3. The angles of a triangle are in the ratio 1 : 3 : 5. Find the measure of each one of the angles. Sol. Sum of three angles of a triangle = 180º Ratio of three angles = 1 : 3 : 5 First angle 180 1 1 3 5 180 1 9 20 º º º Second angle 180 3 9 60 º º Third angle 180 5 9 100 º º Hence, three angles are 20º, 60º and 100º Ans. Q. 4. One of the acute angles of a right triangle is 50º. Find the other acute angle. Sol. Sum of three angles of a right triangle = 180º Sum of two acute angles = 180º – 90º = 90º Measure of one angle = 50º Second acute angle = 90º – 50º = 40º Ans. Q. 5. One of the angles of a triangle is 110º and the other two angles are equal. What is the measure of each of these equal angles ? Sol. Let the measure of each of the equal angles be xº. Then, xº + xº + 110º = 180º (Angle sum property of a triangle) 2xº + 110º = 180º 2xº = 180º – 110º = 70º Page 2 ( ) EXERCISE 16 A Q.1. Take three non-collinear points A, B and C on a page of your notebook. Join AB, BC and CA. What figure do you get ? Name : (i) the side opposite to C (ii) the angle opposite to the side BC (iii) the vertex opposite to the side CA (iv) the side opposite to the vertex B A C B Sol. A, B and C are three non-collinear points in a plane. AB, BC and CA are joined. A C B (i) The side opposite C is AB (ii) The angle opposite to the side BC is A (iii) The vertex opposite to the side CA is B (iv) The side opposite to the vertex B is CA Q.2. The measures of two angles of a triangle are 72º and 58º. Find the measure of the third angle. Sol. The measures of two angles of a triangle are 72º and 58º But measure of three angles of a triangle is 180º Third angle will be = 180 – (72º + 58º) = 180º – 130º = 50º Q. 3. The angles of a triangle are in the ratio 1 : 3 : 5. Find the measure of each one of the angles. Sol. Sum of three angles of a triangle = 180º Ratio of three angles = 1 : 3 : 5 First angle 180 1 1 3 5 180 1 9 20 º º º Second angle 180 3 9 60 º º Third angle 180 5 9 100 º º Hence, three angles are 20º, 60º and 100º Ans. Q. 4. One of the acute angles of a right triangle is 50º. Find the other acute angle. Sol. Sum of three angles of a right triangle = 180º Sum of two acute angles = 180º – 90º = 90º Measure of one angle = 50º Second acute angle = 90º – 50º = 40º Ans. Q. 5. One of the angles of a triangle is 110º and the other two angles are equal. What is the measure of each of these equal angles ? Sol. Let the measure of each of the equal angles be xº. Then, xº + xº + 110º = 180º (Angle sum property of a triangle) 2xº + 110º = 180º 2xº = 180º – 110º = 70º xº º º F H G I K J 70 2 35 . The measure of each of the equal angles is 35º. Q. 6. If one angle of a triangle is equal to the sum of the other two, show that the triangle is a right triangle. Sol. Let the three angles of a triangle be A, B, C. Then, A = B + C Adding A to both sides, we get A + A = A + B + C 2 A = 180º (Angle sum property of a triangle) F H G I K J A 180º 2 90º . One of the angles of the triangle is a right angle. Hence, the triangle is a right triangle. Q. 7. In a ABC, if 3 A = 4 B = 6 C, calculate the angles. Sol. In a ABC, . . . 3 A = 4 B = 6 C = 1 (say) A = 1 3 B = 1 4 C = 1 6 Ratio 1 3 1 4 1 6 : : 4 3 2 12 : : (LCM of 3, 4, 6 = 12) = 4 : 3 : 2 Sum of angles ABC = 180º A = 180º 4 4 + 3 + 2 180 4 9 80 º º B = 180º 3 9 60º C = 180º 2 9 40º Hence, angles of ABC are 80º, 60º and 40º. Ans. Q. 8. Look at the figure given below. State for each triangle whether it is acute, right or obtuse. Sol. (i) It is obtuse triangle. (ii) It is acute triangle. (iii) It is right triangle. (iv) It is obtuse triangle. Q. 9. In the given figure some triangles have been given. State for each triangle whether it is scalene, isosceles or equilateral. C B 130° A 60° 60° 60° E F D Q R P 90° 92° Y Z X Page 3 ( ) EXERCISE 16 A Q.1. Take three non-collinear points A, B and C on a page of your notebook. Join AB, BC and CA. What figure do you get ? Name : (i) the side opposite to C (ii) the angle opposite to the side BC (iii) the vertex opposite to the side CA (iv) the side opposite to the vertex B A C B Sol. A, B and C are three non-collinear points in a plane. AB, BC and CA are joined. A C B (i) The side opposite C is AB (ii) The angle opposite to the side BC is A (iii) The vertex opposite to the side CA is B (iv) The side opposite to the vertex B is CA Q.2. The measures of two angles of a triangle are 72º and 58º. Find the measure of the third angle. Sol. The measures of two angles of a triangle are 72º and 58º But measure of three angles of a triangle is 180º Third angle will be = 180 – (72º + 58º) = 180º – 130º = 50º Q. 3. The angles of a triangle are in the ratio 1 : 3 : 5. Find the measure of each one of the angles. Sol. Sum of three angles of a triangle = 180º Ratio of three angles = 1 : 3 : 5 First angle 180 1 1 3 5 180 1 9 20 º º º Second angle 180 3 9 60 º º Third angle 180 5 9 100 º º Hence, three angles are 20º, 60º and 100º Ans. Q. 4. One of the acute angles of a right triangle is 50º. Find the other acute angle. Sol. Sum of three angles of a right triangle = 180º Sum of two acute angles = 180º – 90º = 90º Measure of one angle = 50º Second acute angle = 90º – 50º = 40º Ans. Q. 5. One of the angles of a triangle is 110º and the other two angles are equal. What is the measure of each of these equal angles ? Sol. Let the measure of each of the equal angles be xº. Then, xº + xº + 110º = 180º (Angle sum property of a triangle) 2xº + 110º = 180º 2xº = 180º – 110º = 70º xº º º F H G I K J 70 2 35 . The measure of each of the equal angles is 35º. Q. 6. If one angle of a triangle is equal to the sum of the other two, show that the triangle is a right triangle. Sol. Let the three angles of a triangle be A, B, C. Then, A = B + C Adding A to both sides, we get A + A = A + B + C 2 A = 180º (Angle sum property of a triangle) F H G I K J A 180º 2 90º . One of the angles of the triangle is a right angle. Hence, the triangle is a right triangle. Q. 7. In a ABC, if 3 A = 4 B = 6 C, calculate the angles. Sol. In a ABC, . . . 3 A = 4 B = 6 C = 1 (say) A = 1 3 B = 1 4 C = 1 6 Ratio 1 3 1 4 1 6 : : 4 3 2 12 : : (LCM of 3, 4, 6 = 12) = 4 : 3 : 2 Sum of angles ABC = 180º A = 180º 4 4 + 3 + 2 180 4 9 80 º º B = 180º 3 9 60º C = 180º 2 9 40º Hence, angles of ABC are 80º, 60º and 40º. Ans. Q. 8. Look at the figure given below. State for each triangle whether it is acute, right or obtuse. Sol. (i) It is obtuse triangle. (ii) It is acute triangle. (iii) It is right triangle. (iv) It is obtuse triangle. Q. 9. In the given figure some triangles have been given. State for each triangle whether it is scalene, isosceles or equilateral. C B 130° A 60° 60° 60° E F D Q R P 90° 92° Y Z X Sol. (i) It is an isosceles triangle as it has two equal sides. (ii) It is an isosceles triangle as it has two equal sides. (iii) It is a scalene triangle as its sides are different in length. (iv) It is an equilateral triangle as its all sides are equal. (v) It is an equilateral triangles as its angles are equal, so its sides will also be equal. (vi) It is an isosceles triangle as its two base angles are equal, so its two sides are equal. (vii) It is a scalene triangle as its angles are different, so its sides will also be different or unequal. Q.10. Draw a ABC. Take a point D on BC. Join AD How many triangles do you get ? Name them. C B A D Sol. In ABC, D is a point on BC and AD is joined Now we get triangles ABC, ABD and ADC Q. 11. Can a triangle have : (i) Two right angles (ii) Two obtuse angles (iii) Two acute angles (iv) Each angles more than 60º (v) Each angles less than 60º (vi) Each angles equal to 60º Sol. (i) No (ii) No (iii) Yes (iv) No (v) No (vi) Yes. Q. 12. Fill in the blanks : (i) A triangle has ............ sides, ............ angles and ............ vertices. (ii) The sum of the angles of a triangle is............ . (iii) The sides of a scalene triangle are of ............ lengths. (iv) Each angle of an equilateral triangle measures............ . (v) The angles opposite to equal sides of an isosceles triangle are............ . (vi) The sum of the lengths of the sides of a triangle is called its............ . Sol. (i) three, three, three. (ii) 180º (iii) different (iv) 60º (v) equal (vi) perimeter. ( ) EXERCISE 16 B Objective questions Mark ( ) against the correct answer in each of following. Q. 1. How many parts does a triangle have ? (a) 2 (b) 3 (c) 6 (d) 9 Sol. (c) . . . It has three sides and three angles i.e. six. Q. 2. With the angles given below, in which case the construction of triangle is possible? L Page 4 ( ) EXERCISE 16 A Q.1. Take three non-collinear points A, B and C on a page of your notebook. Join AB, BC and CA. What figure do you get ? Name : (i) the side opposite to C (ii) the angle opposite to the side BC (iii) the vertex opposite to the side CA (iv) the side opposite to the vertex B A C B Sol. A, B and C are three non-collinear points in a plane. AB, BC and CA are joined. A C B (i) The side opposite C is AB (ii) The angle opposite to the side BC is A (iii) The vertex opposite to the side CA is B (iv) The side opposite to the vertex B is CA Q.2. The measures of two angles of a triangle are 72º and 58º. Find the measure of the third angle. Sol. The measures of two angles of a triangle are 72º and 58º But measure of three angles of a triangle is 180º Third angle will be = 180 – (72º + 58º) = 180º – 130º = 50º Q. 3. The angles of a triangle are in the ratio 1 : 3 : 5. Find the measure of each one of the angles. Sol. Sum of three angles of a triangle = 180º Ratio of three angles = 1 : 3 : 5 First angle 180 1 1 3 5 180 1 9 20 º º º Second angle 180 3 9 60 º º Third angle 180 5 9 100 º º Hence, three angles are 20º, 60º and 100º Ans. Q. 4. One of the acute angles of a right triangle is 50º. Find the other acute angle. Sol. Sum of three angles of a right triangle = 180º Sum of two acute angles = 180º – 90º = 90º Measure of one angle = 50º Second acute angle = 90º – 50º = 40º Ans. Q. 5. One of the angles of a triangle is 110º and the other two angles are equal. What is the measure of each of these equal angles ? Sol. Let the measure of each of the equal angles be xº. Then, xº + xº + 110º = 180º (Angle sum property of a triangle) 2xº + 110º = 180º 2xº = 180º – 110º = 70º xº º º F H G I K J 70 2 35 . The measure of each of the equal angles is 35º. Q. 6. If one angle of a triangle is equal to the sum of the other two, show that the triangle is a right triangle. Sol. Let the three angles of a triangle be A, B, C. Then, A = B + C Adding A to both sides, we get A + A = A + B + C 2 A = 180º (Angle sum property of a triangle) F H G I K J A 180º 2 90º . One of the angles of the triangle is a right angle. Hence, the triangle is a right triangle. Q. 7. In a ABC, if 3 A = 4 B = 6 C, calculate the angles. Sol. In a ABC, . . . 3 A = 4 B = 6 C = 1 (say) A = 1 3 B = 1 4 C = 1 6 Ratio 1 3 1 4 1 6 : : 4 3 2 12 : : (LCM of 3, 4, 6 = 12) = 4 : 3 : 2 Sum of angles ABC = 180º A = 180º 4 4 + 3 + 2 180 4 9 80 º º B = 180º 3 9 60º C = 180º 2 9 40º Hence, angles of ABC are 80º, 60º and 40º. Ans. Q. 8. Look at the figure given below. State for each triangle whether it is acute, right or obtuse. Sol. (i) It is obtuse triangle. (ii) It is acute triangle. (iii) It is right triangle. (iv) It is obtuse triangle. Q. 9. In the given figure some triangles have been given. State for each triangle whether it is scalene, isosceles or equilateral. C B 130° A 60° 60° 60° E F D Q R P 90° 92° Y Z X Sol. (i) It is an isosceles triangle as it has two equal sides. (ii) It is an isosceles triangle as it has two equal sides. (iii) It is a scalene triangle as its sides are different in length. (iv) It is an equilateral triangle as its all sides are equal. (v) It is an equilateral triangles as its angles are equal, so its sides will also be equal. (vi) It is an isosceles triangle as its two base angles are equal, so its two sides are equal. (vii) It is a scalene triangle as its angles are different, so its sides will also be different or unequal. Q.10. Draw a ABC. Take a point D on BC. Join AD How many triangles do you get ? Name them. C B A D Sol. In ABC, D is a point on BC and AD is joined Now we get triangles ABC, ABD and ADC Q. 11. Can a triangle have : (i) Two right angles (ii) Two obtuse angles (iii) Two acute angles (iv) Each angles more than 60º (v) Each angles less than 60º (vi) Each angles equal to 60º Sol. (i) No (ii) No (iii) Yes (iv) No (v) No (vi) Yes. Q. 12. Fill in the blanks : (i) A triangle has ............ sides, ............ angles and ............ vertices. (ii) The sum of the angles of a triangle is............ . (iii) The sides of a scalene triangle are of ............ lengths. (iv) Each angle of an equilateral triangle measures............ . (v) The angles opposite to equal sides of an isosceles triangle are............ . (vi) The sum of the lengths of the sides of a triangle is called its............ . Sol. (i) three, three, three. (ii) 180º (iii) different (iv) 60º (v) equal (vi) perimeter. ( ) EXERCISE 16 B Objective questions Mark ( ) against the correct answer in each of following. Q. 1. How many parts does a triangle have ? (a) 2 (b) 3 (c) 6 (d) 9 Sol. (c) . . . It has three sides and three angles i.e. six. Q. 2. With the angles given below, in which case the construction of triangle is possible? L (a) 30º, 60º, 70º (b) 50º, 70º, 60º (c) 40º, 80º, 65º (d) 72º, 28º, 90º Sol. (b) . . . Sum of three angles of a triangle is 180º. Q. 3. The angles of a triangle are in the ratio 2 : 3 : 4. The largest angle is (a) 60º (b) 80º (c) 76º (d) 84º Sol. (b) . . . Largest angle 180 4 2 3 4 180 4 9 80 º º º . Q. 4. The two angles of a triangle are complementary. The third angle is (a) 60º (b) 45º (c) 36º (d) 90º Sol. (d) . . . A triangle has 180º and if two angles are complementary i.e. sum of two angles is 90º, then third angle will be 180º – 90º = 90º. Q. 5. One of the base angles of an isosceles triangle is 70º The vertical angle is (a) 60º (b) 80º (c) 40º (d) 35º Sol. (c) . . . Sum of three angles is 180º and sum of two equal angles = 70º + 70º = 140º, then third angle will be 180º – 140º = 40º. Q. 6. A triangle having sides of different lengths is called (a) an isosceles triangle (b) an equilateral triangle (c) a scalene triangle (d) a right triangle Sol. (c) . . . A scalene triangle has different sides. Q.7. In an isosceles ABC, the bisectors of B and C meet at a point O. If A = 40º, then BOC = ? (a) 110º (b) 70º (c) 130º (d) 150º Sol. In an isosceles ABC, B = C and bisector of B and C meet at O and A = 40º O A 40º B C B = C = 2 º 40 º 180 = 2 º 140 = 70º 2 1 B = 2 1 C = 2 º 70 = 35º Now in OBC BOC + OBC + OCB = 180º BOC + 2 1 B + 2 1 C = 180º BOC + 35º + 35º = 180º BOC = 180º – 70º = 110º (a) Q.8. The side of a triangle are in the ratio 3 : 2 : 5 and its perimeter is 30 cm. The length of the longest side is (a) 20 cm (b) 15 cm (c) 10 cm (d) 12 cm Sol. Side of a trianlge are in the ratio 3 : 2 : 5 and perimter = 30 m Length of longest side = 5 2 3 5 30 = 10 5 30 cm = 15 cm (b) Q.9. Two angles of a trianlge measure 30º and Page 5 ( ) EXERCISE 16 A Q.1. Take three non-collinear points A, B and C on a page of your notebook. Join AB, BC and CA. What figure do you get ? Name : (i) the side opposite to C (ii) the angle opposite to the side BC (iii) the vertex opposite to the side CA (iv) the side opposite to the vertex B A C B Sol. A, B and C are three non-collinear points in a plane. AB, BC and CA are joined. A C B (i) The side opposite C is AB (ii) The angle opposite to the side BC is A (iii) The vertex opposite to the side CA is B (iv) The side opposite to the vertex B is CA Q.2. The measures of two angles of a triangle are 72º and 58º. Find the measure of the third angle. Sol. The measures of two angles of a triangle are 72º and 58º But measure of three angles of a triangle is 180º Third angle will be = 180 – (72º + 58º) = 180º – 130º = 50º Q. 3. The angles of a triangle are in the ratio 1 : 3 : 5. Find the measure of each one of the angles. Sol. Sum of three angles of a triangle = 180º Ratio of three angles = 1 : 3 : 5 First angle 180 1 1 3 5 180 1 9 20 º º º Second angle 180 3 9 60 º º Third angle 180 5 9 100 º º Hence, three angles are 20º, 60º and 100º Ans. Q. 4. One of the acute angles of a right triangle is 50º. Find the other acute angle. Sol. Sum of three angles of a right triangle = 180º Sum of two acute angles = 180º – 90º = 90º Measure of one angle = 50º Second acute angle = 90º – 50º = 40º Ans. Q. 5. One of the angles of a triangle is 110º and the other two angles are equal. What is the measure of each of these equal angles ? Sol. Let the measure of each of the equal angles be xº. Then, xº + xº + 110º = 180º (Angle sum property of a triangle) 2xº + 110º = 180º 2xº = 180º – 110º = 70º xº º º F H G I K J 70 2 35 . The measure of each of the equal angles is 35º. Q. 6. If one angle of a triangle is equal to the sum of the other two, show that the triangle is a right triangle. Sol. Let the three angles of a triangle be A, B, C. Then, A = B + C Adding A to both sides, we get A + A = A + B + C 2 A = 180º (Angle sum property of a triangle) F H G I K J A 180º 2 90º . One of the angles of the triangle is a right angle. Hence, the triangle is a right triangle. Q. 7. In a ABC, if 3 A = 4 B = 6 C, calculate the angles. Sol. In a ABC, . . . 3 A = 4 B = 6 C = 1 (say) A = 1 3 B = 1 4 C = 1 6 Ratio 1 3 1 4 1 6 : : 4 3 2 12 : : (LCM of 3, 4, 6 = 12) = 4 : 3 : 2 Sum of angles ABC = 180º A = 180º 4 4 + 3 + 2 180 4 9 80 º º B = 180º 3 9 60º C = 180º 2 9 40º Hence, angles of ABC are 80º, 60º and 40º. Ans. Q. 8. Look at the figure given below. State for each triangle whether it is acute, right or obtuse. Sol. (i) It is obtuse triangle. (ii) It is acute triangle. (iii) It is right triangle. (iv) It is obtuse triangle. Q. 9. In the given figure some triangles have been given. State for each triangle whether it is scalene, isosceles or equilateral. C B 130° A 60° 60° 60° E F D Q R P 90° 92° Y Z X Sol. (i) It is an isosceles triangle as it has two equal sides. (ii) It is an isosceles triangle as it has two equal sides. (iii) It is a scalene triangle as its sides are different in length. (iv) It is an equilateral triangle as its all sides are equal. (v) It is an equilateral triangles as its angles are equal, so its sides will also be equal. (vi) It is an isosceles triangle as its two base angles are equal, so its two sides are equal. (vii) It is a scalene triangle as its angles are different, so its sides will also be different or unequal. Q.10. Draw a ABC. Take a point D on BC. Join AD How many triangles do you get ? Name them. C B A D Sol. In ABC, D is a point on BC and AD is joined Now we get triangles ABC, ABD and ADC Q. 11. Can a triangle have : (i) Two right angles (ii) Two obtuse angles (iii) Two acute angles (iv) Each angles more than 60º (v) Each angles less than 60º (vi) Each angles equal to 60º Sol. (i) No (ii) No (iii) Yes (iv) No (v) No (vi) Yes. Q. 12. Fill in the blanks : (i) A triangle has ............ sides, ............ angles and ............ vertices. (ii) The sum of the angles of a triangle is............ . (iii) The sides of a scalene triangle are of ............ lengths. (iv) Each angle of an equilateral triangle measures............ . (v) The angles opposite to equal sides of an isosceles triangle are............ . (vi) The sum of the lengths of the sides of a triangle is called its............ . Sol. (i) three, three, three. (ii) 180º (iii) different (iv) 60º (v) equal (vi) perimeter. ( ) EXERCISE 16 B Objective questions Mark ( ) against the correct answer in each of following. Q. 1. How many parts does a triangle have ? (a) 2 (b) 3 (c) 6 (d) 9 Sol. (c) . . . It has three sides and three angles i.e. six. Q. 2. With the angles given below, in which case the construction of triangle is possible? L (a) 30º, 60º, 70º (b) 50º, 70º, 60º (c) 40º, 80º, 65º (d) 72º, 28º, 90º Sol. (b) . . . Sum of three angles of a triangle is 180º. Q. 3. The angles of a triangle are in the ratio 2 : 3 : 4. The largest angle is (a) 60º (b) 80º (c) 76º (d) 84º Sol. (b) . . . Largest angle 180 4 2 3 4 180 4 9 80 º º º . Q. 4. The two angles of a triangle are complementary. The third angle is (a) 60º (b) 45º (c) 36º (d) 90º Sol. (d) . . . A triangle has 180º and if two angles are complementary i.e. sum of two angles is 90º, then third angle will be 180º – 90º = 90º. Q. 5. One of the base angles of an isosceles triangle is 70º The vertical angle is (a) 60º (b) 80º (c) 40º (d) 35º Sol. (c) . . . Sum of three angles is 180º and sum of two equal angles = 70º + 70º = 140º, then third angle will be 180º – 140º = 40º. Q. 6. A triangle having sides of different lengths is called (a) an isosceles triangle (b) an equilateral triangle (c) a scalene triangle (d) a right triangle Sol. (c) . . . A scalene triangle has different sides. Q.7. In an isosceles ABC, the bisectors of B and C meet at a point O. If A = 40º, then BOC = ? (a) 110º (b) 70º (c) 130º (d) 150º Sol. In an isosceles ABC, B = C and bisector of B and C meet at O and A = 40º O A 40º B C B = C = 2 º 40 º 180 = 2 º 140 = 70º 2 1 B = 2 1 C = 2 º 70 = 35º Now in OBC BOC + OBC + OCB = 180º BOC + 2 1 B + 2 1 C = 180º BOC + 35º + 35º = 180º BOC = 180º – 70º = 110º (a) Q.8. The side of a triangle are in the ratio 3 : 2 : 5 and its perimeter is 30 cm. The length of the longest side is (a) 20 cm (b) 15 cm (c) 10 cm (d) 12 cm Sol. Side of a trianlge are in the ratio 3 : 2 : 5 and perimter = 30 m Length of longest side = 5 2 3 5 30 = 10 5 30 cm = 15 cm (b) Q.9. Two angles of a trianlge measure 30º and 25º respectively. The measure of the third angle is (a) 35º (b) 45º (c) 65º (d) 125º Sol. Two angles of a trianlge are 30º and 25º But sum of three angles of a triangle = 180º Third angle = 180º – (30 + 25º) = 180º – 55º = 125º (d) Q.10. Each angle of an equilateral triangle measures (a) 30º (b) 45º (c) 60º (d) 80º Sol. Each angles of an equilateral triangle = 60º as each angle of an equilateral triangle are equal Each angle = 3 º 180 = 60º (c) Q. 11. In the adjoining figure, the point P lies (a) in the interior of ABC (b) in the exterior of ABC (c) on ABC (d) outside ABC C A B P Sol. _ In the figure, P lies on AB Its lies on the ABC (c)Read More

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