Question

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

Answer 1

Answer:

The measure of angle EYH is 25°.

Step-by-step 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

$m\angle EYH=\frac{1}{2}(arc(EV)-arc(EH))=\frac{1}{2}(130-80)=\frac{1}{2}(50)\\ m \angle EYH = 25\°$

Therefore, the measure of angle EYH is 25°.