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) Responses 18 18 98 98 72 72 14

Answer 1

Since ∠1 and ∠3 are a vertical pair, their measures are equal. Thus, we can set the equations equal to each other:

\[ m∠1 = m∠3 \]

Substituting the given expressions:

\[ 4x + 26 = 98 \]

To solve for \(x\), first subtract 26 from both sides:

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

Now, divide both sides by 4:

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

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