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

18
18

72
72

14

Answer 1

In a geometric figure with two intersecting lines, vertical angles are equal. Since \( \angle 1 \) and \( \angle 3 \) are vertical angles, we know that:

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

We are given that \( m\angle 1 = (4x + 26)^\circ \) and \( m\angle 3 = 98^\circ \). Setting those equal to each other gives us the equation:

\[ 4x + 26 = 98 \]

Now, let's solve for \( x \):

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

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

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