Question

Given: mHL =40°, mEV =130°, mVL =110°. Find: m∠EYH.

Answer 1

The measure of angle EYH is 25°.

Explanation:

Notice that ray EY is a tangent and ray VY is a secant.

In this case, we use the theorem that states "the angle formed by a tangent and a secant is half of the difference of the intercepted arcs".

In this case, the intercepted arcs are EH and EV. We know that a whole arc is 360°, so

`arc(EH)=360-40-110-130=80`

Using the theorem, we have

`m\angle EYH=(1)/(2)(arc(EV)-arc(EH))=(1)/(2)(130-80)=(1)/(2)(50)\\ m \angle EYH = 25\°`

Therefore, the measure of angle EYH is 25°.