Page 53 - Ganit Kaushal

Miscellaneous Solved Examples

There are four options (Q. 1 to Q. 16) out of which only one is correct. Choose the correct option.
Ex 1. In the given figure, ∠XYZ cannot be written as (NCERT Exemplar)
(a) ∠Y (b) ∠ZXY

(c) ∠ZYX (d) ∠XYP
Sol. (b) since ∠ZXY represents the angle made at point X.
Ex 2. The number of angles in the given figure is (NCERT Exemplar)
(a) 3 (b) 4
(c) 5 (d) 6
Sol. (d) (i) 40°, (ii) 20°, (iii) 30°, (iv) 40° + 20° = 60°, (v) 20° + 30° = 50°,

(vi) 40° + 20° + 30° = 90°
Ex 3. In the given figure, if point A is shifted to point B along the ray PX such that
PB = 2PA, then the measure of ∠BPY is (NCERT Exemplar)
(a) Greater than 45° (b) 45°
(c) Less than 45° (d) 90°
Sol. (b) is the correct answer.
Ex 4. The measure of the two angles between the hour hand and the minute hand
of a clock at 9 o’clock is (NCERT Exemplar)
(a) 60°, 300° (b) 90°, 270°
(c) 75°, 285° (d) 30°, 330°

Sol. (b) 9 to 12 clockwise: 90°; 9 to 12 anticlockwise: 270°
Ex 5. If a bicycle wheel has 48 spokes, then the angle between a pair of two consecutive spokes is
(NCERT Exemplar)
 1 °  1 °  2  °  2  °
(a) 5 2 (b) 7 2  (c)  11  (d)  15 







360° 1 °
Sol. (b) Angle between a pair of two consecutive spokes = = 7
48° 2
Ex 6. The number of obtuse angles in the given figure is (NCERT Exemplar)
(a) 2 (b) 3
(c) 4 (d) 5
Sol. (d) (i) 20° + 45° + 65° = 130°, (ii) 45° + 65° = 110°, (iii) 65° + 30° = 95°,
(iv) 45° + 65° + 30° = 140°, (v) 20° + 45° + 65° + 30° = 160°
Ex 7. If the sum of two angles is equal to an obtuse angle, then which of the following is not possible?
(a) One obtuse angle and one acute angle (b) Two acute angles
(c) One right and one acute angle (d) Two right angles
Sol. (d) Two right angles = 90° + 90° = 180°, a straight line
Ex 8. Which of the following has no end points?
(a) A line (b) A ray (c) A line segment (d) None of these.

Sol. (a) A line

Lines and Angles 51