Question

∠1 and angle, 2∠2 are vertical angles. If mangle, 1, equals, left parenthesis, 3, x, plus, 21, right parenthesis, degrees∠1=(3x+21)
∘
and mangle, 2, equals, left parenthesis, 4, x, minus, 2, right parenthesis, degrees∠2=(4x−2)
∘
, then find the value of x.

Answer 1

Since angles \( \angle 1 \) and \( \angle 2 \) are vertical angles, they are equal. Thus, we can set their measures equal to each other:

\[
3x + 21 = 4x - 2
\]

To solve for \( x \), we will start by isolating \( x \). First, subtract \( 3x \) from both sides:

\[
21 = 4x - 3x - 2
\]

This simplifies to:

\[
21 = x - 2
\]

Next, add \( 2 \) to both sides:

\[
21 + 2 = x
\]

So,

\[
x = 23
\]

Therefore, the value of \( x \) is \( \boxed{23} \).