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

\[ m∠1 = m∠3 \]

Substituting the given expressions:

\[ 3x - 25 = 104 \]

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

1. Add 25 to both sides of the equation:

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

   \[ 3x = 129 \]

2. Divide both sides by 3:

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

   \[ x = 43 \]

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