∠1 and angle, 2∠2 are vertical angles. If mangle, 1, equals, left parenthesis, 4, x, minus, 8, right parenthesis, degrees∠1=(4x−8)

Question

∘
and mangle, 2, equals, left parenthesis, 3, x, plus, 18, right parenthesis, degrees∠2=(3x+18)
∘
, then find the value of x.

Answer 1

Since angles 1 and 2 are vertical angles, their measures are equal. Therefore, we can set the expressions for the angles equal to each other:

\[ 4x - 8 = 3x + 18 \]

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

1. Subtract \(3x\) from both sides:

\[ 4x - 3x - 8 = 18 \] \[ x - 8 = 18 \]

2. Next, add 8 to both sides:

\[ x = 18 + 8 \] \[ x = 26 \]

Thus, the value of \(x\) is \(\boxed{26}\).