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**Ques 1: ****Find the complement of each of the following angles: **** ****Ans: **Complementary angle = 90Â° - given angle**(i) **Complement of 20Â° = 90Â° -20Â° = 70Â°**(ii) **Complement of 63Â° = 90Â° -63Â° = 27Â°**(iii) **Complement of 57Â° =90Â° -57Â° =33Â°**Ques 2: ****Find the supplement of each of the following angles: **

**Ans: **Supplementary angle = 180Â° - given angle**(i) **Supplement of 105Â° = 180Â° - 105Â° = 75Â°**(ii) **Supplement of 87Â° = 180Â°-87Â° = 93Â°**(iii) **Supplement of 154Â° = 180Â°-154Â° = 26Â°**Ques 3: ****Identify which of the following pairs of angles are complementary and which are supplementary: ****(i) 65Â°, 115Â° ****(ii) 63Â°, 27Â° ****(iii) 112Â°, 68Â°****(iv) 130Â°, 50Â° ****(v) 45Â°, 45Â° ****(vi) 80Â°,10Â°****Ans: **If sum of two angles is 180^{o} , then they are called supplementary angles.

If sum of two angles is 90^{o} , then they are called complementary angles.

**(i) **65Â° + 115Â° = 180Â° These are supplementary angles.**(ii)** 63Â° 4- 27Â° = 90Â° These are complementary angles.**(iii)** 112Â° + 68Â° = 180Â° These are supplementary angles.**(iv)** 130Â° + 50Â° = 180Â° These are supplementary angles.**(v)** 45Â° + 45Â° = 90Â° These are complementary angles.**(vi)** 80Â° +10Â° = 90Â° These are complementary angles.**Ques 4: ****Find the angle which is equal to its complement. ****Ans: **Let one of the two equal complementary angles be x.

âˆ´ x + x = 90Â°

â‡’ 2x = 90Â°

â‡’ x = 90Â°/2 = 45Â°

Thus, 45Â° is equal to its complement.**Ques 5: ****Find the angle which is equal to its supplement. ****Ans: **Let x be two equal angles of its supplement.

Therefore,

x + x = 180Â° [Supplementary angles]

â‡’ 2x = 180Â°

â‡’ x = 180Â°/2 = 90Â°

Thus, 90Â° is equal to its supplement.**Ques 6: ****In the given figure,** âˆ **1 and **âˆ **2 are supplementary angles. If **âˆ **1 is decreased, what changes should take place in **âˆ **2 so that both the angles still remain supplementary? **

**Ans: **If âˆ 1 is decreased then, âˆ 2 will increase with the same measure, so that both the angles still remain supplementary.**Ques 7: ****Can two angles be supplementary if both of them are: ****(i) acute ****(ii) obtuse ****(iii) right? ****Ans: ****(i)** No, because sum of two acute angles is less than 180^{o}**(ii)** No, because sum of two obtuse angles is more than 180^{o}**(iii)** Yes, because sum of two right angles is 180^{o}**Ques 8: ****An angle is greater than 45**^{o}** . Is its complementary angle greater than 45**^{o}** or equal to 45**^{o}** or less than 45**^{o}** ? ****Ans: **Let the complementary angles be x and y, i.e.p x+ y = 90Â°

It is given that x > 45Â°

Adding y both sides, x + y > 45Â° + y

â‡’ 90Â° > 45Â° + y

â‡’ 90 - 45Â° > y

â‡’ y < 45Â°

Thus, its complementary angle is less than 45Â°.**Ques 9: In the adjoining figure:**

**Ans: ****(i)** Vertically opposite angles, âˆ 1 and âˆ 4; âˆ 5 and âˆ 2 + âˆ 3.**(ii) **Linear pairs âˆ 1 and âˆ 5; âˆ 5 and âˆ 4.**Ques 11: ****In the following figure, is âˆ 1 adjacent to âˆ 2? Give reasons. **

**Ans: ****âˆ **1 and **âˆ **2 are not adjacent angles because their vertex is not common.**Ques 12: ****Find the values of the angles x,y and z in each of the following:**** ****Ans: ****(i) **x = 55Â° [Vertically opposite angles]

Now 55Â°+ y = 180Â° [Linear pair]

â‡’ y = 180Â° - 55Â° = 125Â°

Also y = z = 125Â° [Vertically opposite angles]**(ii) **40Â°+ x + 25Â° = 180Â° [Angles on straight line]

â‡’ 65Â°+ x = 180Â°

â‡’ x = 180Â°- 65Â° = 115Â°

Now 40Â° + y = 180Â° [Linear pair]

â‡’ y -180Â° - 40Â° = 140Â° ........(i)

Also y + z = 180Â° [Linear pair]

â‡’ 140Â°+r = 180Â° [From equation (i)]

â‡’ z = 180Â°-140Â° = 40Â°

Thus, x = 115Â°,y = 140Â° and z = 40Â°.**Ques 13: ****Fill in the blanks: ****(i) If two angles are complementary, then the sum of their measures is _______________. ****(ii) If two angles are supplementary, then the sum of their measures is _______________. ****(iii) Two angles forming a linear pair are _______________. ****(iv) If two adjacent angles are supplementary, they form a _______________.****(v) If two lines intersect a point, then the vertically opposite angles are always _______________. ****(vi) If two lines intersect at a point and if one pair of vertically opposite angles are acute angles, then the other pair of vertically opposite angles are _______________. ****Ans: ****(i)** 90Â°**(ii)** 180Â°**(iii)** supplementary**(iv)** linear pair**(v)** equal **(vi)** obtuse angles**Ques 14: ****In the adjoining figure, name the following pairs of angles: ****(i) Obtuse vertically opposite angles. ****(ii) Adjacent complementary angles. ****(iii) Equal supplementary angles. ****(iv) Unequal supplementary angles. ****(v) Adjacent angles that do not form a linear pair. ****Ans:** (i) Obtuse vertically opposite angles means greater than 90â€™ and equal âˆ AOD = âˆ BOC.**(ii)** Adjacent complementary angles means angles have common vertex, common arm, non-common arms are on either side of common arm and sum of angles is 90Â°.**(iii)** Equal supplementary angles means sum of angles is 180Â° and supplement angles are equal.**(iv)** Unequal supplementary angles means sum of angles is 180Â° and supplement angles are unequal.

i.e., âˆ AOE, âˆ EOC; âˆ AOD, âˆ DOC and âˆ AOB, âˆ BOC**(v)** Adjacent angles that do not form a linear pair mean, angles have common ray but the angles in a linear pair are not supplementary.

i.e., âˆ AOB, âˆ AOE; âˆ AOE, âˆ EOD and âˆ EOD, âˆ COD**Exercise 5.2 ****Ques 1: ****State the property that is used in each of the following statements: ****(i) If aâ•‘b, then âˆ 1 = âˆ 5.****(ii) If âˆ 4 = âˆ 6, then aâ•‘b.****(iii) If âˆ 4 + âˆ 5 + 180Â°, then aâ•‘b****Ans: ****(i)** Given, aâ•‘b, then âˆ 1 = âˆ 5 [Corresponding angles]

If two parallel lines are cut by a transversal, each pair of corresponding angles are equal in measure.**(ii)** Given, âˆ 4 = âˆ 6, then aâ•‘b [Alternate interior angles]

When a transversal cuts two lines such that pairs of alternate interior angles are equal, the lines have to be parallel.**(iii)** Given, âˆ 4+ âˆ 5= 180Â°, then aâ•‘b [Co-interior Angles]

When a transversal cuts two lines, such that pairs of interior angles on the same side of transversal are supplementary, the lines have to be parallel.**Ques 2: ****In the adjoining figure, identify: ****(i) the pairs of corresponding angles.****(ii) the pairs of alternate interior angles.****(iii) the pairs of interior angles on the same side of the transversal.****(iv) the vertically opposite angles.**

**Ans: ****(i) **The pairs of corresponding angles: âˆ 1, âˆ 5; âˆ 2, âˆ 6; âˆ 4, âˆ 8 and âˆ 3, âˆ 7**(ii)** The pairs of alternate interior angles are: âˆ 3, âˆ 5 and âˆ 2, âˆ 8**(iii)** The pair of interior angles on the same side of the transversal: âˆ 3, âˆ 8 and âˆ 2, âˆ 5**(iv)** The vertically opposite angles are: âˆ 1, âˆ 3; âˆ 2, âˆ 4; âˆ 6, âˆ 8 and âˆ 5, âˆ 7**Ques 3: ****In the adjoining figure, pâ•‘q. Find the unknown angles.**

**Ans: **Given, pâ•‘q and cut by a transversal line,

âˆµ 125Â°+ e = 180Â° [Linear pair]

âˆµ e = 180Â°-125Â° = 55Â° ....(i)

Now e = f = 55Â° [Vertically opposite angles]

Also a = f = 55Â° [Alternate interior angles]

a + b = 180Â° [Linear pair]

â‡’ 55Â° + b = 180Â° [From equation (i)]

â‡’ 6 = 180Â°- 55Â°= 125Â°

Now a = c = 55Â° and b=d = 125Â° [Vertically opposite angles]

Thus, a = 55Â°,b = 125Â°,c = 55Â°, d = 125Â°, e = 55Â° and f = 55Â°.**Ques 4: ****Find the values of x in each of the following figures if l || m.**

**Ans:** (i) Given, lâ•‘m and t is transversal line.

âˆ´ Interior vertically opposite angle between lines l and t = 110Â°.

âˆ´ 110Â° + x = 180Â° [Supplementary angles]

â‡’ x = 180Â° -110Â° = 70Â°**(ii)** Given, lâ•‘m and t is transversal line.

x + 2x = 180 [Interior opposite angles]

â‡’ 3x = 180Â°

â‡’ x = 180Â°/3 = 60Â°**(iii)** Given, lâ•‘m and aâ•‘b.

x = 100Â° [Corresponding angles]**Ques 5: ****In the given figure, the arms of two angles are parallel. If Î”ABC = 70 ^{o} , then find: **

**Ans:** (i) Given, AB â•‘ DE and BC is a transversal line and âˆ ABC = 70Â°

âˆ´ âˆ ABC = âˆ DGC [Corresponding angles]

âˆ DGC = 70Â° ........(i)**(ii)** Given, BC â•‘ EF and DE is a transversal line and âˆ DGC = 70Â°

âˆ´ âˆ DGC = âˆ DEF [Corresponding angles]

âˆ DEF = 70Â° [From equation (i)]**Ques 6: ****In the given figures below, decide whether l is parallel to m. **

**Ans: ****(i)** 126Â°+ 44Â° = 170Â°

lâ•‘m because sum of interior opposite angles should be 180Â°**(ii)** 75Â° + 75Â° = 150Â°

lâ•‘m because sum of angles does not obey the property of parallel lines.**(iii)** 57Â°+123Â° = 180Â°

lâ•‘m due to supplementary angles property of parallel lines.**(iv)** 98Â°+ 72Â° = 170Â°

I is not parallel to m because sum of angles does not obey the property of parallel lines.

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