Question

∠1 and angle, 2∠2 are vertical angles. If mangle, 1, equals, left parenthesis, 6, x, plus, 8, right parenthesis, degrees∠1=(6x+8)
∘
and mangle, 2, equals, left parenthesis, 2, x, plus, 12, right parenthesis, degrees∠2=(2x+12)
∘
, then find the value of x.

Answer 1

Since angles \( \angle 1 \) and \( \angle 2 \) are vertical angles, they are equal. Therefore, we can set the expressions for the angles equal to each other:

\[
6x + 8 = 2x + 12
\]

Now, we'll solve for \( x \). First, subtract \( 2x \) from both sides:

\[
6x - 2x + 8 = 12
\]
\[
4x + 8 = 12
\]

Next, subtract \( 8 \) from both sides:

\[
4x = 12 - 8
\]
\[
4x = 4
\]

Now, divide both sides by \( 4 \):

\[
x = 1
\]

Thus, the value of \( x \) is \( \boxed{1} \).