In a geometric figure two intersecting lines creating four angles. If ∠1

Question

and ∠3
are a vertical pair, m∠1=(4x+26)°
, and m∠3=98°
, what is the value of x
?(1 point)
Responses

98
98

72
72

14
14

18

Answer 1

To find the value of \( x \), we start by recognizing that vertical angles are equal. Given that \( \angle 1 \) and \( \angle 3 \) are vertical angles, we set their measures equal to each other:

\[ m\angle 1 = m\angle 3 \]

Substituting the given expressions:

\[ 4x + 26 = 98 \]

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

1. Subtract 26 from both sides: \[ 4x = 98 - 26 \] \[ 4x = 72 \]

2. Divide by 4: \[ x = \frac{72}{4} \] \[ x = 18 \]

Thus, the value of \( x \) is \( 18 \). The correct answer is:

18