Question

topic quiz b
name
date

1. two vertical angles are labeled as $\angle c$ and $\angle d$. the measure of $\angle c$ is $57.6^\circ$. the measure of $\angle d$ is $(3x + 21)^\circ$.

solve for $x$.
a. 3.8
b. 12.2
c. 33.8
d. 57.6

1. the diagram shows $\overrightarrow{ae}$ intersecting $\overrightarrow{cf}$ and $\overrightarrow{dg}$ at point $b$.

Explanation:

Step1: Recall vertical angles property

Vertical angles are equal, so \( \angle C=\angle D \).
Given \( \angle C = 57.6^\circ \) and \( \angle D=(3x + 21)^\circ \), we set up the equation:
\( 3x+21 = 57.6 \)

Step2: Solve for x

Subtract 21 from both sides:
\( 3x=57.6 - 21 \)
\( 3x = 36.6 \)

Divide both sides by 3:
\( x=\frac{36.6}{3} \)
\( x = 12.2 \)

Answer:

B. 12.2