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

72
72

98
98

18
18

14

Answer 1

To find the value of \( x \), we start with the given information:

• Angles 1 and 3 are vertical angles.
• \( m∠1 = (4x + 26)° \)
• \( m∠3 = 98° \)

Since vertical angles are equal, we can set up the equation:

\[ 4x + 26 = 98 \]

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

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

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

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