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

120
120

37.5

Answer 1

Vertical angles are equal, so we can set the measures of the two angles equal to each other:

\[
m∠2 = m∠4
\]

Given \( m∠2 = 135° \) and \( m∠4 = (4x + 15)° \), we can set up the equation:

\[
135 = 4x + 15
\]

Next, we can solve for \( x \):

1. Subtract 15 from both sides:

\[
135 - 15 = 4x
\]

\[
120 = 4x
\]

2. Divide both sides by 4:

\[
x = \frac{120}{4} = 30
\]

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