Question

Given: m LHE =84°
Find: m∠EYL.

Answer 1

Answer:
`m\angle EYL=96\°`

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 = (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=(1)/(2)(276\°-84\°) \\\\m\angle EYL=96\°`