We are given a quadrilateral QRST inscribed in a circle U. The angles are given as $Q = 79^\circ$, $R = 67^\circ$, $T = (x+96)^\circ$, and $S = (2y+17)^\circ$. We need to find the values of $x$ and $y$.

1. Problem Description

We are given a quadrilateral QRST inscribed in a circle U. The angles are given as $Q = 79^\circ$, $R = 67^\circ$, $T = (x+96)^\circ$, and $S = (2y+17)^\circ$. We need to find the values of $x$ and $y$.

2. Solution Steps

Since the quadrilateral QRST is inscribed in a circle, opposite angles are supplementary. This means that the sum of opposite angles is $180^\circ$.

Therefore, we have:

$Q + S = 180^\circ$

$R + T = 180^\circ$

Using the given values, we can write the equations as:

$79 + (2y+17) = 180$

$67 + (x+96) = 180$

Solving for $y$ in the first equation:

$79 + 2y + 17 = 180$

$96 + 2y = 180$

$2y = 180 - 96$

$2y = 84$

$y = \frac{84}{2}$

$y = 42$

Solving for $x$ in the second equation:

$67 + x + 96 = 180$

$x + 163 = 180$

$x = 180 - 163$

$x = 17$

3. Final Answer

$x = 17$

$y = 42$