Question

in the diagram below , the measure of arc SQ is 160 degrees and the measure of arc PR is 102 degrees . find the value of x .

Answer 1

Given:

The measure of angle of arrc SQ is 160°.

The measure of angle of arc PR is 102°.

The objective is to find the measure of angle x.

Since, the angle x is away from te center of the circle.

Then, the formula to find the value of angle x is,

`x=(PR+SQ)/(2)`

Now, substitute the given values in the above formula.

`\begin{gathered} x=(102+160)/(2) \\ =(262)/(2) \\ =131\degree \end{gathered}`

Hence, the value of x is 131°.