Question

in the diagram below, $odot p$ is circumscribed about quadrilateral $abcd$. what is the value of $x$? a. 98 b. 78 c. 102 d. 82

Explanation:

Step1: Recall cyclic - quadrilateral property

Opposite angles of a cyclic quadrilateral are supplementary. So, $\angle A+\angle C = 180^{\circ}$.

Step2: Set up the equation

We know that $\angle A=x + 10^{\circ}$ and $\angle C=88^{\circ}$. Then, $(x + 10)+88=180$.

Step3: Simplify the equation

$x+98 = 180$.

Step4: Solve for x

Subtract 98 from both sides: $x=180 - 98=78$.

Answer:

B. 78