Question

∠1 and angle, 2∠2 are complementary angles. If m, angle, 1, equals, left parenthesis, x, plus, 1, right parenthesis, degreesm∠1=(x+1)
∘
and m, angle, 2, equals, left parenthesis, 7, x, minus, 15, right parenthesis, degreesm∠2=(7x−15)
∘
, then find the measure of angle, 2∠2.

Answer 1

Since angles \( \angle 1 \) and \( \angle 2 \) are complementary, we have:

\[
m \angle 1 + m \angle 2 = 90^\circ
\]

Given:
- \( m \angle 1 = (x + 1)^\circ \)
- \( m \angle 2 = (7x - 15)^\circ \)

Substituting the expressions for the angles into the complementary angles equation:

\[
(x + 1) + (7x - 15) = 90
\]

Now, combine like terms:

\[
x + 1 + 7x - 15 = 90
\]
\[
8x - 14 = 90
\]

Next, add 14 to both sides:

\[
8x = 104
\]

Now, divide by 8:

\[
x = 13
\]

Now that we found \( x \), we can substitute it back to find \( m \angle 2 \):

\[
m \angle 2 = 7x - 15
\]
\[
m \angle 2 = 7(13) - 15
\]
\[
m \angle 2 = 91 - 15
\]
\[
m \angle 2 = 76
\]

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

\[
\boxed{76^\circ}
\]