Question

what is the value of x? x =

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of interior angles of a triangle is 180°. In triangle PQR, we have two - known angles 6x and 54°. Assume the third - angle is a right - angle (since the line through the center of the circle and the triangle might imply a right - angled triangle situation, if the line is a diameter and the triangle is inscribed in the semi - circle, although not explicitly stated, but a common geometric property). Let's assume the third angle is 90°. Then, 6x+54° + 90°=180°.

Step2: Solve the equation for x

First, simplify the left - hand side of the equation: 6x+144° = 180°. Then, subtract 144° from both sides: 6x=180° - 144° = 36°. Divide both sides by 6: x = $\frac{36^{\circ}}{6}$ = 6°.

Answer:

6