Question

what is the value of x? p x + 15° q 39° r x =

Explanation:

Step1: Recall angle - sum property of a triangle

In \(\triangle PQR\), the sum of interior angles of a triangle is \(180^{\circ}\). Also, since \(PQ\) is a diameter of the circle, \(\angle PRQ = 90^{\circ}\) (angle - in - a - semi - circle property).

Step2: Set up the equation

We know that \((x + 15)+39+90=180\).
First, simplify the left - hand side of the equation: \((x + 15)+39+90=x+(15 + 39+90)=x + 144\).
So, the equation becomes \(x + 144=180\).

Step3: Solve for \(x\)

Subtract 144 from both sides of the equation: \(x=180 - 144\).
\(x = 36\).

Answer:

\(36\)