a quadrilateral is inscribed in circle o. the angle measures of the quadrilateral, in degrees, are given by the expressions shown in the figure. what is the measure of angle c? a. 15° b. 75° c. 165° d. 65°

Question

Accepted Answer

# Explanation:
## Step1: Use the property of cyclic quadrilaterals
In a cyclic quadrilateral, the sum of opposite angles is $180^{\circ}$. So, $\angle A+\angle C = 180^{\circ}$ and $\angle B+\angle D=180^{\circ}$. First, use $\angle B+\angle D = 180^{\circ}$ to find $x$.
$$
\begin{align*}
(4x + 35)+(7x-20)&=180\
4x+7x+35 - 20&=180\
11x+15&=180\
11x&=180 - 15\
11x&=165\
x&=15
\end{align*}
$$
## Step2: Find the measure of $\angle C$
Substitute $x = 15$ into the expression for $\angle C$ ($95-2x$).
$$
\begin{align*}
\angle C&=95-2x\
&=95-2\times15\
&=95 - 30\
&=65^{\circ}
\end{align*}
$$

# Answer:
D. $65^{\circ}$

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QUESTION IMAGE

Question

Explanation:

Step1: Use the property of cyclic quadrilaterals

Step2: Find the measure of \(\angle C\)

Answer: