Question

∠1 and angle, 2∠2 are vertical angles. If mangle, 1, equals, left parenthesis, 7, x, minus, 19, right parenthesis, degrees∠1=(7x−19)
∘
and mangle, 2, equals, left parenthesis, 6, x, plus, 3, right parenthesis, degrees∠2=(6x+3)
∘
, then find the measure of angle, 2∠2.

Answer 1

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

\[
7x - 19 = 6x + 3
\]

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

1. Subtract \(6x\) from both sides:

\[
7x - 6x - 19 = 3
\]

This simplifies to:

\[
x - 19 = 3
\]

2. Next, add 19 to both sides:

\[
x = 22
\]

Now that we have the value of \(x\), we can substitute it back into either angle's expression to find the measure of angle ∠2.

Using the expression for ∠2:

\[
\text{m}\angle 2 = 6x + 3
\]

Substituting \(x = 22\):

\[
\text{m}\angle 2 = 6(22) + 3
\]

\[
\text{m}\angle 2 = 132 + 3
\]

\[
\text{m}\angle 2 = 135
\]

Thus, the measure of angle ∠2 is \(135\) degrees.