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
[tex]arc(EH)=360-40-110-130=80[/tex]
Using the theorem, we have
[tex]m\angle EYH=\frac{1}{2}(arc(EV)-arc(EH))=\frac{1}{2}(130-80)=\frac{1}{2}(50)\\ m \angle EYH = 25\°[/tex]
Therefore, the measure of angle EYH is 25°.
