Question

Given: m LHE =84° Find: m∠EYL.

Answer 1

Answer: $m\angle EYL=96\°$

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:

$Angle\ formed \ by\ two\ tangents = \frac{1}{2}(Difference\ of\ Intercepted\ Arcs)$

According to the information given in the exercise, you know that:

$Angle\ formed \ by\ two\ tangents = m\angle EYL\\\\Difference\ of\ Intercepted\ Arcs=m LVE-mLHE$

Since there are 360 degrees in a circle, you can determine that:

$mLVE=360\°-mLHE\\\\mLVE=360\°-84\°\\\\mLVE=276\°$

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:

$m\angle EYL=\frac{1}{2}(276\°-84\°) \\\\m\angle EYL=96\°$