We have a circle with an inscribed angle $x$ that subtends an arc. The intercepted arc's measure on the circle is $150^\circ$. We are asked to find the measure of angle $x$.

1. Problem Description

We have a circle with an inscribed angle $x$ that subtends an arc. The intercepted arc's measure on the circle is $150^\circ$. We are asked to find the measure of angle $x$.

2. Solution Steps

The measure of an inscribed angle is half the measure of its intercepted arc.

Therefore, $x = \frac{1}{2} \times 150^\circ$.

$x = 75^\circ$

3. Final Answer

$x = 75^\circ$