Exercise 5.4
Ques 1: What is the measure of
(i) a right angle?
(ii) a straight angle?
Ans: (i) 90^{o}
(ii) 180^{o}
Ques 2: Say True or False:
(a) The measure of an acute angle < 90.
(b) The measure of an obtuse angle < 90.
(c) The measure of a reflex angle > 180.
(d) The measure of on complete revolution = 360.
(e) If m∠A = 53^{o} and m∠B = 35^{o} then m∠A > m∠B.
Ans: (a) True
(b) False
(c) True
(d) True
(e) True
Ques 3: Write down the measure of:
(a) some acute angles
(b) some obtuse angles
(give at least two examples of each)
Ans: (a) 35^{o},^{ }20^{o}
(b) 110^{o}, 135^{o}
Ques 4: Measure the angles give below, using the protractor and write down the measure:
Ans: (a) 40^{o}
(b) 130^{o}
(c) 90^{o}
(d) 60^{o}
Ques 5: Which angle has a large measure? First estimate and then measure:
Measure of angle A = ?
Measure of angle B = ?
Ans: ∠B has larger measure. ∠A = 40^{o} and ∠B = 65^{o}
Ques 6: From these two angles which has larger measure? Estimate and then confirm by measuring them:
Ans: Second angle has larger measure.
Ques 7: Fill in the blanks with acute, obtuse, right or straight:
(a) An angle whose measure is less than that of a right angle is ________________.
(b) An angle whose measure is greater than that of a right angle is ________________.
(c) An angle whose measure is the sum of the measures of two right angles is ________________.
(d) When the sum of the measures of two angles is that of a right angle, then each one of them is ________________.
(e) When the sum of the measures of two angles is that of a straight angle and if one of them is acute then the other should be ________________.
Ans: (a) acute angle
(b) obtuse angle
(c) straight angle
(d) acute angle
(e) obtuse angle
Ques 8: Find the measure of the angle shown in each figure. (First estimate with your eyes and then find the actual measure with a protractor).
Ans: (i) 30^{o}
(ii) 120^{o}
(iii) 60^{o}
(iv) 150^{o}
Ques 9: Find the angle measure between the hands of the clock in each figure:
Ans: (i) 90 (Right angle)
(ii) 30 (Acute angle)
(iii) 180 (Straight angle)
Ques 10: Investigate:
In the given figure, the angle measure 30. Look at the same figure through a magnifying glass. Does the angle becomes larger? Does the size of the angle change?
Ans: No, the measure of angle will be same.
Ques 11: Measure and classify each angle:
Angle  Measure  Type 
∠AOB 


∠AOC 


∠BOC 


∠DOC 


∠DOA 


∠DOB 


Ans:
Angle  ∠AOB  ∠AOC  ∠BOC  ∠DOC  ∠DOA  ∠DOB 
Measure  40^{°}  130^{°}  90^{°}  90^{°}  140^{°}  180^{°} 
Type  Acute  Obtuse  Right  Right  Obtuse  Straight 
Exercise 5.5
Ques 1: Which of the following are models for perpendicular lines:
(a) The adjacent edges of a table top.
(b) The lines of a railway track.
(c) The line segments forming the letter ‘L’.
(d) The letter V.
Ans: (a) Perpendicular
(b) Not perpendicular
(c) Perpendicular
(d) Not perpendicular
Ques 2: Let be the perpendicular to the line segment . Let and intersect in the point A. What is the measure of ∠PAY?
Ans:
Ques 3: There are two “setsquares” in your box. What are the measures of the angles that are formed at their corners? Do they have any angle measure that is common?
Ans: One setsquare has 45 ,90 ,45 and other setsquare has 60 ,90 ,30 . They have 90 as common angle.
Ques 4: Study the diagram. The line l is perpendicular to line m.
(a) Is CE = EG?
(b) Does PE bisect CG?
(c) Identify any two line segments for which PE is the perpendicular bisector.
(d) Are these true?
(i) AC > FG
(ii) CD = GH
(iii) BC < EH
Ans: (a) Yes, both measure 2 units.
(b) Yes, because CE = EG
(d) (i) True, (ii) True, (iii) True
Exercise 5.6
Ques 1: Name the types of following triangles:
(a) Triangle with lengths of sides 7 cm, 8 cm and 9 cm.
(b) ΔABC with AB = 8.7 cm, AC = 7 cm and BC = 6 cm.
(c) ΔPQR such that PQ = QR = PR = 5 cm.
(d) ΔDEF with m∠D = 90^{o}
(e) ΔXYZ with m∠Y = 90^{o} and XY = YZ
(f) ΔLMN with m∠L = 30^{o} , m∠M = 70^{o} and m∠N = 80^{o}.
Ans: (a) Scalene triangle
(b) Scalene triangle
(c) Equilateral triangle
(d) Rightangled triangle
(e) Isosceles rightangled triangle
(f) Acuteangled triangle
Ques 2: Match the following:
Measure of Triangle  Types of Triangle 
(i) 3 sides of equal length  (a) Scalene 
(ii) 2 sides of equal length  (b) Isosceles right angle 
(iii) All sides are of different length  (c) Obtuse angle 
(iv) 3 acute angles  (d) Right angle 
(v) 1 right angle  (e) Equilateral 
(vi) 1 obtuse angle  (f) Acute angle 
(vii) 1 right angle with two sides of equal length  (g) Isosceles 
Ans: (i) → (e)
(ii) → (g)
(iii) → (a)
(iv) → (f)
(v) → (d)
(vi) → (c)
(vii) → (b)
Ques 3: Name each of the following triangles in two different ways: (You may judge the nature of angle by observation)
Ans: (a) Acute angled triangle and Isosceles triangle
(b) Rightangled triangle and scalene triangle
(c) Obtuseangled triangle and Isosceles triangle
(d) Rightangled triangle and Isosceles triangle
(e) Equilateral triangle and acute angled triangle
(f) Obtuseangled triangle and scalene triangle
Ques 4: Try to construct triangles using match sticks. Some are shown here.
Can you make a triangle with:
(a) 3 matchsticks?
(b) 4 matchsticks?
(c) 5 matchsticks?
(d) 6 matchsticks? (Remember you have to use all the available matchsticks in each case)
If you cannot make a triangle, think of reasons for it.
Ans: (a) 3 matchsticks This is an acute angle triangle and it is possible with 3 matchsticks to make a triangle because sum of two sides is greater than third side.
(b) 4 matchsticks This is a square, hence with four matchsticks we cannot make triangle.
(c) 5 matchsticks This is an acute angle triangle and it is possible to make triangle with five matchsticks, in this case sum of two sides is greater than third side.
(d) 6 matchsticks This is an acute angle triangle and it is possible to make a triangle with the help of 6 matchsticks because sum of two sides is greater than third side.