Question

In circle O two secants,

ABP and CDP, are drawn to external point P. If mAC = 72°, and mBD = 34°, what is the measure of ∠P?
(1) 19° (3) 53°
(2) 38° (4) 106°

Answer 1

(1)19°

Explanation:

The diagram is drawn and attached below.

Let x=mAC = 72°; and

y=mBD = 34°

By the Angle-Arc relationship, the external angle is half the difference.

`\angle P=(1)/(2)(x^\circ-y ^\circ)\\$Therefore:\\m\angle P=(1)/(2)(72^\circ-34 ^\circ)\\m\angle P=19^\circ`