We are given a cyclic quadrilateral $ABCD$ inscribed in a circle. The angles are given as follows: $\angle A = 14x$, $\angle B = 16x$, $\angle C = 22x$, and $\angle D = 20x$. We need to find the value of $x$ and the measure of angle $C$.
2025/3/28
1. Problem Description
We are given a cyclic quadrilateral inscribed in a circle. The angles are given as follows: , , , and . We need to find the value of and the measure of angle .
2. Solution Steps
Since the quadrilateral is cyclic, opposite angles are supplementary. This means that the sum of opposite angles is .
Thus, we have:
Substituting the given expressions for the angles:
We can also check the other pair of angles:
Now, we can find the measure of angle :