In a geometric figure two intersecting lines creating four angles. If ∠1 and ∠3 are a vertical pair, m∠1=(4x+26)° , and m∠3=98° , what is the value of x ?(1 point)

Question

Responses

1414

18
18

7272

98

Answer 1

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

\[ m∠1 = m∠3 \]

Substituting the given values:

\[ 4x + 26 = 98 \]

Now, 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 \( \boxed{18} \).