Question

Find the measure of the arc or angle indicated. Assume that lines which appear tangent are tangent.

Answer 1

Given:

In the given circle, the measure of major arc TV is 220 degrees.

To find:

The measure of angle TUV.

Solution:

In a circle, the measure central angle of arc is equal to its corresponding arc measure and according to central angle theorem, the measure of subtended angle on an arc is half of the measure of central angle of that arc.

So, the measure of subtended angle is half of the measure of its corresponding arc.

`m\angle TUV=(1)/(2)* \text{Measure of major arc TV}`

`m\angle TUV=(1)/(2)* 220^\circ`

`m\angle TUV=110^\circ`

Therefore, the measure of angle TUV is 110 degrees.