Question

For two vertical angles with measures m∠2=135°
and m∠4=(4x+15)°
, what is the value of x
?(1 point)
Responses

7.5
7.5

30
30

37.5
37.5

120
120

Answer 1

Vertical angles are equal in measure. Therefore, we can set the measures of the two angles equal to each other:

\[
m∠4 = m∠2
\]

Given:

\[
m∠2 = 135°
\]

and

\[
m∠4 = (4x + 15)°
\]

Setting them equal:

\[
135 = 4x + 15
\]

Now, we will solve for \( x \):

1. Subtract 15 from both sides:

\[
135 - 15 = 4x
\]

\[
120 = 4x
\]

2. Divide both sides by 4:

\[
x = \frac{120}{4}
\]

\[
x = 30
\]

Thus, the value of \( x \) is \( 30 \).

Answer: **30**