In a geometric figure two intersecting lines create four angles, where ∠1

Question

and ∠3
are a vertical pair. If m∠1=(3x−25)°
and m∠3=104°
, what is the value of x
?(1 point)

Answer 1

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

\[ m∠1 = m∠3 \]

Substituting the given expressions:

\[ 3x - 25 = 104 \]

To solve for \(x\), first add 25 to both sides:

\[ 3x = 104 + 25 \] \[ 3x = 129 \]

Next, divide both sides by 3:

\[ x = \frac{129}{3} \] \[ x = 43 \]

So the value of \(x\) is \( \boxed{43} \).