Answer: [tex]m\angle EYL=96\°[/tex]
Step-by-step explanation:
For this exercise you need to use the formula for calculate the measure of the angle formed by two tangents intersecting outside of a circle. This is:
[tex]Angle\ formed \ by\ two\ tangents = \frac{1}{2}(Difference\ of\ Intercepted\ Arcs)[/tex]
According to the information given in the exercise, you know that:
[tex]Angle\ formed \ by\ two\ tangents = m\angle EYL\\\\Difference\ of\ Intercepted\ Arcs=m LVE-mLHE[/tex]
Since there are 360 degrees in a circle, you can determine that:
[tex]mLVE=360\°-mLHE\\\\mLVE=360\°-84\°\\\\mLVE=276\°[/tex]
Therefore, knowing these values, you can substitute them into the formula given above and the evaluate, in order to find the measure of the angle EYL. This is:
[tex]m\angle EYL=\frac{1}{2}(276\°-84\°) \\\\m\angle EYL=96\°[/tex]
