An arc subtends a central angle of 110 degrees at the center of a circle. What is the angle subtended by the same arc at any point on the remaining circumference?
Answer and explanation
Correct answer: C. 55 degrees
- Step 1: By circle theorems, the angle subtended by an arc at the center is exactly twice the angle subtended at the circumference. Step 2. Divide central angle by 2: 110 / 2 = 55 degrees. Answer: 55 degrees. Why not the others: 110 degrees assumes equal angles; 70 degrees subtracts from 180; 35 degrees divides 70 by 2.
Practise more Geometry, Mensuration and Mental Ability.
Free questions with an explanation for every one, and full timed Bangladesh Civil Service Preliminary Examination mock tests.
More Geometry, Mensuration and Mental Ability questions
- Two angles are complementary, and their degree measures are in the ratio 2 : 3. What is the degree measure of the larger angle?
- An angle measures such that its supplementary angle is four times its complementary angle. What is the measure of this angle in degrees?
- The three interior angles of a triangle are in the ratio 3 : 4 : 5. What is the degree measure of the largest interior angle?
- What is the degree measure of each exterior angle of a regular octagon (an 8-sided regular polygon)?
- What is the sum of all interior angles of a convex hexagon (a 6-sided polygon)?
- A right-angled triangle has perpendicular legs measuring 9 cm and 12 cm. What is the length of its hypotenuse?