We are given a cyclic quadrilateral QRST inscribed in a circle. We are given that $\angle Q = 95^\circ$, $\angle T = 80^\circ$, $\angle R = x^\circ$, and $\angle S = y^\circ$. We need to find the values of $x$ and $y$.

1. Problem Description

We are given a cyclic quadrilateral QRST inscribed in a circle. We are given that $\angle Q = 95^\circ$, $\angle T = 80^\circ$, $\angle R = x^\circ$, and $\angle S = y^\circ$. We need to find the values of $x$ and $y$.

2. Solution Steps

Since QRST is a cyclic quadrilateral, opposite angles are supplementary, meaning their sum is $180^\circ$. Therefore, we have:

$\angle Q + \angle S = 180^\circ$

$\angle R + \angle T = 180^\circ$

We are given $\angle Q = 95^\circ$ and $\angle T = 80^\circ$. We can substitute these values into the equations above.

$95^\circ + y^\circ = 180^\circ$

$x^\circ + 80^\circ = 180^\circ$

Now we can solve for $x$ and $y$.

$y = 180 - 95 = 85$

$x = 180 - 80 = 100$

Therefore, $x = 100$ and $y = 85$.

3. Final Answer

x = 100

y = 85