Question

Angle A is circumscribed about circle O. What is the measure of angle A?

Answer 1

Given:

Angle A is circumscribed about circle O.

m∠CDB = 48°

To find:

The measure of angle A.

Solution:

OC and OB are radius of circle O.

AC and AB are tangents of circle O.

The angle between tangent and radius is always 90°.

⇒ m∠OCA = 90° and m∠OBA = 90°

The angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle.

⇒ m∠COB = 2 × m∠CDB

⇒ m∠COB = 2 × 48°

⇒ m∠COB = 96°

Sum of all the angles of quadrilateral is 360°.

m∠BAC + m∠OCA + m∠COB + m∠OBA = 360°

m∠BAC + 90° + 96° + 90° = 360°

m∠BAC + 276° = 360°

Subtract 276° from both sides.

m∠BAC = 84°

The measure of ∠A is 84°.

Answer 2

Answer:

Step-by-step explanation:

The measure is 84 degrees