Geometry (Railway Maths) (Part – V)

Total Questions: 50

41. In a triangle ABC, incenter is at O. Find the angle ∠BAC if ∠BOC = 110°. [RRB NTPC 03/02/2021 (Evening)]

Correct Answer: (b) 40°
Solution:

42. Find the degree measure of an angle subtended at the centre of a circle of radius 28 cm by an arc of length 22 cm. [RRB NTPC 04/02/2021 (Evening)]

Correct Answer: (b) 45°
Solution:

43. Find the ratio of the measure of an angle of a regular pentagon to that of a regular octagon. [RRB NTPC 04/02/2021 (Evening)]

Correct Answer: (b) 4 : 5
Solution:

44. The area of an isosceles right angle triangle is 81 cm². Find the length of its hypotenuse. [RRB NTPC 04/02/2021 (Evening) ]

Correct Answer: (b) 18 cm
Solution:

45. If one angle of a parallelogram is 39° less than twice the smallest angle, then the smallest angle of the parallelogram is: [RRB NTPC 08/02/2021 (Morning)]

Correct Answer: (c) 73°
Solution:

Let the smallest angle = x Then , the largest angle will be = 180° - x But , the same equals to (2x -39°) Sum of All angles of parallelogram = 360° x + x + (2x - 39°) + (2x - 39°) = 360° ⇒ X = 73°

46. What is the sum of the angle complementary to 15° and the angle supplementary to 125°? [RRB NTPC 09/02/2021 (Morning)]

Correct Answer: (c) 130°
Solution:

The sum of two complementary angles = 90° The sum of two supplementary angles = 180°
Given , one complementary angle = 15°, so that another angle = 90° - 15° = 75° One supplementary angle = 125° , so that another angle = 180° - 125° = 55° Then the sum of another angles = 75° + 55° = 130°

47. In triangle ABC, ∠A is 12° more than the measure of ∠C. The measure of ∠B is 4 times as great as the measure of ∠C. What are the measures of angles A, B and C respectively? [RRB NTPC 09/02/2021 (Morning)]

Correct Answer: (b) 40°, 112°, 28°
Solution:

48. The sum of two angles is 155° and their difference is π/2, the value of the greater angle (in radians) is..? [RRB NTPC 09/02/2021 (Evening) ]

Correct Answer: (b) 49π / 72
Solution:

49. The 4 angles of a pentagon are 70°, 110°, 135° and 95°. Find the measure of the fifth angle of the pentagon. [RRB NTPC 09/02/2021 (Evening)]

Correct Answer: (c) 130°
Solution:

Sum of all angles of a pentagon = 180(5 - 2) = 540°
Sum of 4 angles = 70 + 110 + 135 + 95 = 410°
5th angle = 540 - 410 = 130°

50. The radius of the circle in which a central angle of 60° intercepts an arc of length 35 cm is: [RRB NTPC 10/02/2021 (Evening)]

Correct Answer: (d) 105/π cm
Solution: