Question

you are given an inscribed quadrilateral $wxyz$ with $mangle w = 120^{circ}$ and $mangle x = 60^{circ}$. find the measures of $angle y$ and $angle z$. use the keypad to enter your answers in the boxes. the measure of $angle y$ is degrees. the measure of $angle z$ is degrees.

Explanation:

Step1: Recall property of cyclic quadrilateral

In a cyclic (inscribed) quadrilateral, opposite angles are supplementary, i.e., the sum of opposite - angle measures is 180°.

Step2: Find measure of ∠Y

∠W and ∠Y are opposite angles. Given \(m\angle W = 120^{\circ}\), using the supplementary - angle property \(m\angle Y=180 - m\angle W\). So \(m\angle Y = 180-120=60^{\circ}\).

Step3: Find measure of ∠Z

∠X and ∠Z are opposite angles. Given \(m\angle X = 60^{\circ}\), using the supplementary - angle property \(m\angle Z=180 - m\angle X\). So \(m\angle Z = 180 - 60=120^{\circ}\).

Answer:

The measure of ∠Y is 60 degrees.
The measure of ∠Z is 120 degrees.