Question

The sun rises between two mountain peaks. The edge of one mountain peak (right) forms a tangent with the sun. The other does not. What is the measure of the arc of the sun that is showing given that y=113º. Note: you are solving for the arc measure, not the arc length. Round your answer to one decimal place, if necessary.

Answer 1

Check the picture below.

Answer 2

226°

Explanation:

According to the Tangent and Intersected Chord Theorem, if a tangent and a chord intersect at a point on a circle, then the measure of each angle formed is one-half the measure of its intercepted arc.

Therefore, if y = 113°, then y is one-half of the intercepted arc x.:

`y=(1)/(2)m\overset\frown{x}`

`2y=m\overset\frown{x}`

`2(113^(\circ))=m\overset\frown{x}`

`m\overset\frown{x}=226^(\circ)`

Therefore, the measure of arc x is 226°.