We are given a circle with an inscribed angle $x$ and an exterior angle of $76^\circ$. We need to find the values of angle $x$ and the intercepted arc $y$.

1. Problem Description

We are given a circle with an inscribed angle $x$ and an exterior angle of $76^\circ$. We need to find the values of angle $x$ and the intercepted arc $y$.

2. Solution Steps

First, let's find the measure of the intercepted arc by the $76^\circ$ angle. The measure of an exterior angle is half the difference of the intercepted arcs. Let $y$ be the measure of the intercepted arc by the angle $76^{\circ}$. Let's assume the other intercepted arc is $0^\circ$. Then,

$76 = \frac{1}{2} y$

Multiply both sides by 2:

$152 = y$

The inscribed angle $x$ intercepts arc $y$. The measure of an inscribed angle is half the measure of the intercepted arc. So,

$x = \frac{1}{2}y$

$x = \frac{1}{2}(152)$

$x = 76$

3. Final Answer

$x = 76$

$y = 152$