Option A:
m∠B = 28°
Solution:
Given ABC is a triangle on the circle.
m∠A = 62°
The angle subtended by a diameter or a semicircle on any point of circle is 90°.
AB is a diameter and C is the angle subtended on a diameter.
Therefore, m∠C = 90°.
Triangle sum property:
Sum of the angles of the triangle = 180°
m∠A + m∠B + m∠C = 180°
62° + m∠B + 90° = 180°
m∠B + 152° = 180°
m∠B = 180° – 152°
m∠B = 28°
The measure of angle B is 28°.
Hence Option A is the correct answer.
