Question

Use the diagram below to solve for X. Assume that all segments that appear to be tangent are tangent.

Answer 1

`x=20^(\circ)`

1) In this problem, we can see two Secant lines coming from a point outside the circle.

2) Let's sketch this out to better grasp how to deal with that:

From this situation, we can write out the following relation:

`\begin{gathered} m\angle PRT=(1)/(2)(mRT-mQR) \\ \end{gathered}`

So, we can plug into that the given data, the measure of the angle and the measure of the arcs:

`\begin{gathered} m\angle PRT=(1)/(2)(mRT-mQR) \\ 60^(\circ)=(1)/(2)(8x-2x) \\ 60^(\circ)=4x-x \\ 3x=60^(\circ) \\ (3x)/(3)=(60^(\circ))/(3) \\ x=20^(\circ) \end{gathered}`

Hence, after solving that for x, we can state the answer is:

`x=20^(\circ)`