ANSWER KEY
Multiple Choice questions:
1. B. trapezium
2. D. 5 faces
3. B. 8
4. C. straight angle
5. C. parallelogram
6. A. square
7. B. 9
8. B. acute angle
9. B. 180°
10. C. straight angle
11. B. 12
12. C. 300
13. C. Remains the same
14. B. obtuse angled triangle
15. B. an obtuse angle
Match The Following:
Fill in the blanks:
1. Measure of a complete angle is 360o.
2. The triangle in which two sides are equal is called isosceles triangle.
3. Each of its angles rectangle measures 90o.
4. A cube has 8 vertices.
True /False:
1. True
2. False. in isosceles triangle only two sides are equal.
3. False. For a polygon to be regular, all sides as well as all angles have to be equal.
4. True.
Very Short Answer:
1. In geometry, a tetrahedron is a polyhedron composed of four triangular faces,
three of which meet at each corner or vertex.
2. Straight Angle (180°)
3. Hexagon
Sides of hexagon: AB, BC, CD, DE, EF and FA.
Diagonals of hexagon: AC, AD, AE, BD, BE, BF, CE, CF, and DF
4.
5.
6. (a) 45°
(b) 125°
(c) 90°
(d) ∠1 = 40°, ∠2 = 125° and ∠3 = 95°.
7. An isosceles triangle is any triangle with 2 sides that are equal in length. So, every equilateral triangle
is a special case of an isosceles triangle since not just 2 sides are equal, but all 3 are. But every isosceles
triangle is not equilateral, because you can have 2 sides of equal length and a third side that is either longer
or shorter than those 2 sides. For example, if the triangle is a right-angle triangle and the two sides that meet
to make the right angle are the same length, then the 3rd side would be longer than those two.
8.
9. Three line segments are used to make a triangle.
10. The measure of straight angle is 180°.
Short Answer:
1.(a) ∠QOY = acute angle.
(b) ∠YOP = obtuse angle.
(c) ∠ROX = right angle.
(d) ∠QOX = reflex angle.
(e) ∠POQ = straight angle.
2. ∠a = 180° -129° = 51°
∠b = 180°– (51° + 92°)
= 180° – 143° = 37°
∠c = 180°– 88° = 92°
∠d = 180°– 152° = 28°
∠e = 180°– 143° = 37°
∠f= 180°– (∠e + ∠d)
= 180° – (37° + 28°)
= 180°- 65°= 115°
∠g = 180°–∠f = 180°– 115° = 65°
3. (a) All sides are different. So, it is a scalene triangle.
(b) Lengths of two sides of the triangle are same. So, it is an isosceles triangle.
(c) All sides are unequal and one angle is right angle. So it is scalene right angled triangle.
(d) Two sides of this triangle are equal. So, it is an isosceles triangle.
4. (a) Scalene triangle.
(b) Equilateral triangle.
(c) Isosceles triangle
LongAnswer:
1. (a) Here, F = 5, E = 9 and V = 6
∴ V + F = E + 2
⇒ 6 + 5 = 9 + 2
⇒ 11 = 11
Hence, verified.
(b) Here, F = 6, E = 12 and V = 8
∴ V + F = E + 2
⇒ 8 + 6 = 12 + 2
⇒ 14 = 14
Hence, verified.
(c) Here, F = 7, E = 15 and V = 10
∴ V + F = E + 2
⇒ 10 + 7 = 15 + 2
⇒ 17 = 17
Hence, verified.
(d) Here, F = 4, E = 6 and V = 4
∴ V + F = E + 2
⇒ 4 + 4 = 6 + 2
⇒ 8 = 8
Hence, verified.
2.
3. Given that ∠A = 40°
(i) ∠DAB + ∠ABC = 180° (adjacent angles)
⇒ 40° + ∠ABC = 180°
⇒∠ABC = 180°– 40° = 140°
Hence, ∠x = 140°
(ii) ∠x + ∠y = 180° (adjacent angles)
⇒ 140° + ∠y = 180°
⇒∠y = 180°– 140° = 40°
Hence, ∠y = 40°
(iii) ∠y + ∠z – 180° (adjacent angles)
⇒ 40° + ∠z = 180°
⇒∠z = 180°– 40° = 140°
Hence, ∠z = 140°
(iv) ∠x + ∠s = 180° (straight angles)
⇒ 140° + ∠s = 180°
⇒∠s = 180°– 140° = 40°
Hence, ∠s = 40°
(v) ∠m + ∠z = 180° (straight angles)
⇒∠m + 140° = 180°
⇒∠m = 180°– 140° = 40°
4. (i) Sum of the three angles of a triangle = 180°
∴ 2x + 30° + 60°– x + 3x – 10° = 180°
⇒ (2x – x + 3x) + (30° + 60°– 10°) = 180°
⇒ 4x + 80° = 180°
⇒ 4x = 180°– 80°
⇒ 4x = 100°
∴ x = 10004 = 25°
∴ Measure of the angles are:
(i) (2x + 30)° – 2 × 25° + 30° = 80°
(ii) (60 – x)° = 60° – 25° = 35°
(iii) (3x – 10)° = 3 × 25° – 10° = 75° – 10° = 65°
Hence, x = 25° and the angles of the triangles are: 80°, 35° and 65°.
Assertion and Reason Answers:
(1)(a) Both A and R are true and R is the correct explanation of A
(2)(b) Both A and R are true but R is not the correct explanation of A