Q1. What is the measure of
(i) a right angle?
Ans: The measure of a right angle is 90^{o}
(ii) a straight angle?
Ans: The measure of a straight angle is 180^{o}
Q2. 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; the measure of an acute angle is less than 90^{o}
(b) False; the measure of an obtuse angle is more than 90^{o} but less than 180^{o}
(c) True; the measure of a reflex angle is more than 180^{o}
(d) True; the measure of one complete revolution is 360^{o}
(e) True; ∠A is greater than ∠B
Q3. Write down the measure of:
(a) some acute angles
(b) some obtuse angles
(give at least two examples of each)
Ans: (a) The measures of an acute angle are 50°, 65°
(b) The measures of obtuse angle are 110°, 175°
Q4. Measure the angles given below using the Protractor and write down the measure:
Ans: (a) The measure of an angle is 45°
(b) The measure of an angle is 120°
(c) The measure of an angle is 90°
(d) The measures of angles are 60°, 90° and 130°
Q5. 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 = 68^{o}
Q6. From these two angles which has larger measure? Estimate and then confirm by measuring them:
Ans: Second angle has larger measure.
The measures of these angles are 45^{o} and 55^{o}.
Q7. Fill in the blanks with acute, obtuse, right or straight:
(a) An angle whose measure is less than that of a right angle is ________________.
Ans: acute angle
(b) An angle whose measure is greater than that of a right angle is ________________.
Ans: obtuse angle
(c) An angle whose measure is the sum of the measures of two right angles is ________________.
Ans: straight angle
(d) When the sum of the measures of two angles is that of a right angle, then each one of them is ________________.
Ans: acute angle
(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: obtuse angle
Q8. 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: The measures of the angles shown in the above figures are 40^{o}, 130^{o}, 65^{o} and 135^{o}
Q9. 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)
Q10. Investigate:
In the given figure, the angle measure 30^{o}. 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.
Q11. Measure and classify each angle:
Ans:
Q1. 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
Q2. Let be the perpendicular to the line segment . Let and intersect in the point A. What is the measure of ∠PAY?
Ans: We will be using the concept of perpendicular lines to solve this.
Since PQ ⊥ XY Therefore, ∠PAY = 90°
Q3. 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 60°,90°, 30° and other setsquare has 45° ,90° ,45°. They have 90° as common angle.
Q4. 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
Q1. 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
Q2. Match the following:
Ans: (i) → (e)
(ii) → (g)
(iii) → (a)
(iv) → (f)
(v) → (d)
(vi) → (c)
(vii) → (b)
Q3. Name each of the following triangles in two different ways: (You may judge the nature of angle by observation)
Ans: (i) Acuteangled and isosceles triangle
(ii) Rightangled and scalene triangle
(iii) Obtuseangled and isosceles triangle
(iv) Rightangled and isosceles triangle
(v) Equilateral and acuteangled triangle
(vi) Obtuseangled and scalene triangle
Q4. 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.
1. What are some examples of elementary shapes? 
2. How are elementary shapes useful in everyday life? 
3. How can elementary shapes be used to teach children about geometry? 
4. What is the difference between a regular and irregular polygon? 
5. How can understanding elementary shapes help with problemsolving? 

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