Question

Find the measure of ZP. P 510 139° mZP= O

Answer 1

A circle with intersecting secant and tangent is given. It is required to find the measure of P.

Recall the Intersecting Secant Angles Theorem: If two secants or tangents intersect outside of the circle, the measure of the angle at their intersection is half the difference between the measures of the arcs they intercept in the circle.

It then follows from the figure by this theorem:

`m\angle P=(1)/(2)(139^(\circ)-51^(\circ))`

Evaluate the expression:

`m\angle P=(1)/(2)(88^(\circ))=44^(\circ)`

Hence, the required angle is 44º.

The required angle is 44º.