For two vertical angles with measures m∠2=135°

Question

and m∠4=(4x+15)°
, what is the value of x
?(1 point)
Responses

30
30

120
120

7.5
7.5

37.5

Answer 1

Vertical angles are congruent, which means their measures are equal. Given that \( m∠2 = 135° \) and \( m∠4 = (4x + 15)° \), we can set them equal to each other:

\[ 135 = 4x + 15 \]

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

1. Subtract 15 from both sides:

\[ 135 - 15 = 4x \]

\[ 120 = 4x \]

2. Divide by 4:

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

\[ x = 30 \]

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