Geometry - Quantitative Aptitude
Q11. An angle is two-third of its supplement. The measure of the angle is
(a) 300
(b) 450
(c) 580
(d) 720
Answer: (d) 720
Let, the angle be x
∴ Supplement of x = 1800 - x
A/Q x = 2/3 (1800 - x)
⇒ 3x = 3600 - 2x
⇒ 5x = 3600
⇒ x = 720
Q12. In the given figure, straight lines AB and CD intersect at O. If ∠x = 3∠y, then ∠y = ?
(a) 200
(b) 400
(c) 450
(d) 600
Answer: (c) 450
We have
∠x + ∠y = 1800
⇒ 3∠y + ∠y = 1800
⇒ 4∠y = 1800
⇒ ∠y = 450
Q13. Two supplementary angles are in the ratio 2 : 4. The smaller angle measures
(a) 450
(b) 600
(c) 750
(d) 900
Answer: (b) 600
Let, the angles be 2x, 4x
A/Q 2x + 4x = 1800
⇒ 6x = 1800
⇒ x = 300
∴ Smaller angle = 2 X 300 = 600
Q14. An angle is 200 more than its complement. The measure of an angle is
(a) 550
(b) 650
(c) 700
(d) 730
Answer: (a) 550
Let, the measure of the angle be x0
Its complement = 900 - x0
A/Q x = 900 - x + 200
⇒ 2x = 1100
⇒ x = 550
Q15. How many angles are made by 5 rays shown in the figure ?
(a) 5
(b) 7
(c) 10
(d) 12
Answer: (c) 10
The angles are
∠AOB, ∠AOC, ∠AOD, ∠AOE, ∠BOC, ∠BOD, ∠BOE, ∠COD, ∠COE, ∠DOE
Total no. of angles = 10
Q16. In the given figure, l1 || l2 and ∠A = 700, then ∠C = ?
(a) 600
(b) 900
(c) 1100
(d) 1250
Answer: (c) 1100
l1 || l2
∴ ∠A = ∠B
∴ ∠B = 700
A/Q, ∠C + ∠B = 1800
⇒ ∠C = 1800 - ∠B = 1800 - 700 = 1100
Q17. In the given figure, ∠AOD = 900. What is the measure of ∠COB.
(a) 450
(b) 900
(c) 1050
(d) 1800
Answer: (b) 900
We have
∠AOD = ∠COB [Opposite angle]
⇒ 900 = ∠COB
∴ ∠COB = 900
Q18. In the given figure, AOB is a straight line, ∠AOC = (5x + 10)0, ∠BOC = (3x - 22)0, the value of x is
(a) 240
(b) 270
(c) 350
(d) 380
Answer: (a) 240
We have
(5x + 10)0 + (3x - 22)0 = 1800
⇒ 8x = 1800 + 220 - 100
⇒ 8x = 1920
⇒ x = 240
Q19. If Δ PQR is an isosceles triangle with ∠R = 900 and RQ = 6 cm, then PQ = ?
(a) 4√2 cm
(b) 6√2 cm
(c) 7√2 cm
(d) 9√2 cm
Answer: (b) 6√2 cm
We have
PR = RQ
⇒ PR = 6 cm
Now PQ2 = PR2 + RQ2 = 62 + 62 = 36 + 36 = 72
∴ PQ = √72 = 6√2 cm
Q20. In a cyclic squad ABCD, ∠A = 700, then ∠C = ?
(a) 600
(b) 900
(c) 1050
(d) 1100
Answer: (d) 1100
We have
∠A + ∠C = 1800
⇒ ∠C = 1800 - ∠A = 1800 - 700 = 1100
Practice Test Exam