133k views
2 votes
Find the values of the variables and the measures of the indicated angles. (help)

Find the values of the variables and the measures of the indicated angles. (help)-example-1
User JArgente
by
7.6k points

1 Answer

2 votes

Answer:

x = 30

Explanation:

You want the measure of the acute angle where a tangent meets a chord that intercepts an arc of 300°.

Inscribed angle

An angle inscribed in a circle has half the measure of the arc it intercepts.

If one leg of that inscribed angle degenerates in length to zero, then the "inscribed" angle becomes the angle between the remaining chord and the tangent to one end of that chord.

In other words, the measure of the angle marked x° is half the measure of the arc it intercepts.

x° = 1/2(360° -300°) = 1/2(60°)

x° = 30°

The value of the variable x is 30.

User Chbrown
by
6.7k points