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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

37.5
37.5

120
120

30

1 answer

Since ∠2 and ∠4 are vertical angles, their measures are equal. Therefore, we can set up the equation:

\[ m∠2 = m∠4 \]

Substituting the given measures:

\[ 135° = (4x + 15)° \]

Now we can solve for \( x \):

  1. Subtract 15 from both sides: \[ 135 - 15 = 4x \] \[ 120 = 4x \]

  2. Divide both sides by 4: \[ x = \frac{120}{4} \] \[ x = 30 \]

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