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

Question

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