Question

5. Circle O is shown below. The diagram is not drawn to scale. (1 point)

What is the measure of angle BAC?

53.5°

146°

36.5°

1070

Answer 1

Given:

m∠AOB = 73°

To find:

The measure of ∠BAC.

Solution:

O is the center of the circle.

OA, OB and OC are radii of the circle.

⇒ OA = OB = OC

In ΔAOB,

OA = OB

Angle opposite to equal sides are equal.

⇒ m∠OAB = m∠OBA ----------- (1)

Sum of all angles of a triangle = 180°

m∠OAB + m∠OBA + m∠AOB = 180°

m∠OAB + m∠OAB + 73° = 180°  (using (1))

2 m∠OAB + 73° = 180°

Subtract 73° from both sides, we get

2 m∠OAB = 107°

Divide by 2 on both sides, we get

m∠OAB = 53.5°

m∠BAC = m∠OAB

m∠BAC = 53.5°

Therefore measure of angle BAC is 53.5°.