Question

∠1 and angle, 2∠2 are vertical angles. If mangle, 1, equals, left parenthesis, 2, x, plus, 16, right parenthesis, degrees∠1=(2x+16)
∘
and mangle, 2, equals, left parenthesis, 6, x, minus, 8, right parenthesis, degrees∠2=(6x−8)
∘
, then find the measure of angle, 2∠2.

Answer 1

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

\[
2x + 16 = 6x - 8
\]

To solve for \( x \), we first isolate the terms involving \( x \) on one side of the equation. We can start by subtracting \( 2x \) from both sides:

\[
16 = 6x - 2x - 8
\]

This simplifies to:

\[
16 = 4x - 8
\]

Next, we add \( 8 \) to both sides:

\[
16 + 8 = 4x
\]

So we have:

\[
24 = 4x
\]

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

\[
x = 6
\]

Now that we have \( x \), we can find the measure of \( \angle 2 \) using the expression for \( \angle 2 \):

\[
\angle 2 = 6x - 8
\]

Substituting \( x = 6 \):

\[
\angle 2 = 6(6) - 8
\]

Calculating this gives:

\[
\angle 2 = 36 - 8 = 28
\]

Thus, the measure of \( \angle 2 \) is:

\[
\boxed{28} \text{ degrees}
\]