Page 295 - Ganit Kaushal

II. 1. 15 2. Square 3. Square 4. 91 8. (a) ∠FST > ∠NML (b) ∠YWX > ∠BOA
III. 1. True 2. False (gives squares) 3. True (c) ∠COD > ∠ZXY (d) ∠XYZ > ∠COD

2
4. True 5. False (it gives 100 ) 9. (a) AB and CD are two intersecting lines and O is
IV. 1. Because they can be represented with the help of the point of intersection.

triangle of dots. (b) PM ⊥ AB

2. Sequence of centered hexagonal numbers; Sequence of (c) AB and CD are parallel lines.

cubes. Exercise 2.3
3. 1, 4, 9, 16, 25 ……; Sequence of squares. 1. acute angle 2. 10°
4. 195 (Hint: 33 + 39 + 54 + 69) 3. (a) acute angle (b) right angle
(c) straight angle (d) obtuse angle
Chapter 2: Lines and Angles
(e) reflex angle (f) complete angle
Exercise 2.1 4. (a) acute angle (b) obtuse angle

1. (a) both (b) AB (c) endpoints (c) right angle (d) straight angle
(d) AB (e) ending (e) reflex angle (f) reflex angle
2. (a) l, m; l, n; m, n (g) acute angle (h) obtuse angle
(b) l, p; m, p; n, p; l, q; m, q; n, q; l, r; m, r; n, r; p, q; 5. (a) ∠a and ∠c are acute; ∠b is obtuse
p, r; q, r. (b) ∠y is acute; ∠x and ∠z are obtuse
(c) n, r, q (c) ∠s and ∠q are acute; ∠p is obtuse; ∠r is reflex
(d) A, B, C; A, H, I, D; D, E, F, G; C, I, E; B, H, F 6. ∠AXB = 65°, ∠EXD = 45°, ∠DXC = 45°,

3. The line is a straight set of points that extends in ∠CXB = 25°, ∠DXB = 70° 7. 15°
opposite directions without end points. Line segment Exercise 2.4
is a part of a line between two end points. 1. (a) 90° (b) 180° (c) 45° (d) 135°
4. (a) True (b) True (c) False (only one) 2. 90°, clockwise 3. North 4. East
5. Infinite many number of lines. 5. (a) straight angle (b) acute angle
6. Only one (c) right angle (d) obtuse angle
7. Exactly one 6. 150° 7. 9 right angles
8. (a) CD, DE (b) AB, BC, BE Miscellaneous Exercise 2.5
(c) AD, BD, CE, FD (d) F 1. (b) 2. (a) 3. (d) 4. (b)
9. (a) (b) 5. (b) 6. (b) 7. (a) 8. (d)
9. (b) 10. (a)
11. (a) Perpendicular (b) Less than
(c) Greater than (d) Greater than
(c) (d) (e) Equal to
12. (a) True
(b) False; The measure of an obtuse angle is > 90° and
< 180°
Exercise 2.2 (c) True (d) True (e) True (f) True
1. Yes; ∠AOC, ∠BOC (g) False; ( 2 × 30° = 60°, which is also an acute angle)
2. Four; ∠A, ∠B, ∠C, and ∠D (h) True
3. ∠AOB, ∠AOC, ∠AOD, ∠BOC, ∠BOD, ∠COD (i) False; ( 1 × 130° = 65°, which is not obtuse)
4. (a) rays, common (b) legs 2
(c) OP, OQ (d) vertex (j) False; (Mathematicians divided circle into 360 equal
parts not 180)
(e) interior 13. (a) 60° (b) 30° (c) 150°
5. 3; ∠AOC, ∠AOB, ∠CОВ. 14. 150°, Obtuse; 210°, reflex 15. 75°
6. (a) P, Q and R (b) S, T 16. Chances of error are more because of improper

(c) X, Y, A, B, С. observation, especially, when the difference between
7. (a) ∠AOB (b) ∠FST angles is small.

Answers 293