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

18
18

14

Answer 1

Since ∠1 and ∠3 are a vertical pair, they are equal. Therefore, you can set up the equation:

\[ m∠1 = m∠3 \]

Substituting the given expressions:

\[ 4x + 26 = 98 \]

Now, solve for \( x \):

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

2. Now divide both sides by 4: \[ x = \frac{72}{4} \] \[ x = 18 \]

So the value of \( x \) is 18.