Question

what is the value of x? x = °

Explanation:

Step1: Recall cyclic - quadrilateral property

Opposite angles of a cyclic quadrilateral are supplementary. In cyclic quadrilateral $PQRS$, $\angle P+\angle R = 180^{\circ}$ and $\angle Q+\angle S=180^{\circ}$.

Step2: Set up the equation

We know that $\angle S = 68^{\circ}$ and $\angle Q=x + 28^{\circ}$. Since $\angle Q+\angle S=180^{\circ}$, the equation is $(x + 28)+68=180$.

Step3: Simplify the left - hand side of the equation

$x+28 + 68=x + 96$. So, $x+96 = 180$.

Step4: Solve for x

Subtract 96 from both sides of the equation: $x=180 - 96$.
$x = 84$.

Answer:

$84$