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

14
14

18
18

72
72

98

Answer 1

Since ∠1 and ∠3 are vertical angles, they are equal in measure. Therefore, we can set up the equation:

\[ m∠1 = m∠3 \]

Substituting the given measures:

\[ 4x + 26 = 98 \]

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

1. Subtract 26 from both sides:

\[ 4x = 98 - 26 \] \[ 4x = 72 \]

2. Divide both sides by 4:

\[ x = \frac{72}{4} \] \[ x = 18 \]

Thus, the value of \(x\) is \( \boxed{18} \).