In the given diagram, points P, Q, R, and S lie on a circle. If PQ = QS and angle PSQ = 80 degrees, what is the measure of angle QRS?

• We are asked to calculate $\angle QRS$.
• We are given that $|PQ| = |QS|$. This means that triangle $PQS$ is an isosceles triangle.
• From the diagram, the angle $\angle PSQ$ is marked as $80^\circ$.

Since $PQ = QS$, the angles opposite these sides in $\triangle PQS$ are equal.
The angle opposite side $PQ$ is $\angle QSP$.
The angle opposite side $QS$ is $\angle QPS$.
Therefore, $\angle QPS = \angle QSP$.

We are given $\angle PSQ = 80^\circ$, which is the same as $\angle QSP$.
So, $\angle QPS = 80^\circ$.

The points P, Q, R, S lie on the circumference of the circle, forming a cyclic quadrilateral PQRS.
In a cyclic quadrilateral, the sum of opposite angles is $180^\circ$.
The angle opposite to $\angle QRS$ is $\angle QPS$.
Therefore, $\angle QRS + \angle QPS = 180^\circ$.

Substitute the value of $\angle QPS$ from Step 3 into the equation from Step 4:

The value of $\