Question

value: 2
find the measure of the angle given.

a. 30°
b. 120°
c. 50°
d. 80°

Explanation:

Step1: Recall cyclic - quadrilateral property

In a cyclic quadrilateral, the sum of opposite angles is 180°. Here, quadrilateral $E D P F$ is cyclic. $\angle DPF = 100^{\circ}$ and $\angle DEF$ are opposite angles.

Step2: Calculate the measure of $\angle DEF$

Let $\angle DEF=x$. Using the property of cyclic - quadrilaterals, we have $\angle DPF+\angle DEF = 180^{\circ}$. Substituting $\angle DPF = 100^{\circ}$ into the equation: $100^{\circ}+x = 180^{\circ}$. Solving for $x$, we get $x=180^{\circ}-100^{\circ}=80^{\circ}$.

Answer:

d. 80°