Question

∠1 and angle, 2∠2 are vertical angles. If mangle, 1, equals, left parenthesis, 3, x, plus, 22, right parenthesis, degrees∠1=(3x+22)
∘
and mangle, 2, equals, left parenthesis, 7, x, minus, 22, right parenthesis, degrees∠2=(7x−22)
∘
, then find the value of x.

Answer 1

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

\[
3x + 22 = 7x - 22
\]

Now we will solve for \( x \):

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

\[
22 = 7x - 3x - 22
\]
\[
22 = 4x - 22
\]

2. Add \( 22 \) to both sides:

\[
22 + 22 = 4x
\]
\[
44 = 4x
\]

3. Divide both sides by \( 4 \):

\[
x = \frac{44}{4}
\]
\[
x = 11
\]

Thus, the value of \( x \) is \( \boxed{11} \).