in a geometric figure 2 intersecting lines create 4 angles, where <1 and <3 are a vertical. If m<1 = ( 3x - 25 ) and m<3 = 104, wut is da value of x?

Answer 1

Since angles \( \angle 1 \) and \( \angle 3 \) are vertical angles, they are equal. Therefore, we can set their measures equal to each other.

We know:

• \( m\angle 1 = 3x - 25 \)
• \( m\angle 3 = 104 \)

Setting them equal gives us the equation:

\[ 3x - 25 = 104 \]

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

\[ 3x = 104 + 25 \]

\[ 3x = 129 \]

Next, divide both sides by 3:

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

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