Question

In the figure O is the centre of the circle and AB is a diameter. angle ∠BOC = 90° . The measure ∠OAC is:

• A. 50°
• B. 25°
• C. 35°
• D. 40°

Answer 1

Answer:

B. 25°

OA = OC, triangle △AOC is an isosceles triangle. In an isosceles triangle, the angles opposite the equal sides are also equal. Therefore, ∠OAC=∠OCA = X.

∠AOC = 180 - ∠BOC

= 180 - 50

= 130

Total angle in triangle AOC is 180

∠AOC + ∠ OAC + ∠ COA = 180

130 + X = X = 180

2X = 50

X = 25