Question

∠1 and angle, 2∠2 are complementary angles. If m, angle, 1, equals, left parenthesis, x, plus, 2, right parenthesis, degreesm∠1=(x+2)
∘
and m, angle, 2, equals, left parenthesis, x, minus, 26, right parenthesis, degreesm∠2=(x−26)
∘
, then find the measure of angle, 1∠1.

Answer 1

Complementary angles add up to \(90^\circ\). Given the measures of the angles:

\[
m∠1 = (x + 2)^\circ
\]
\[
m∠2 = (x - 26)^\circ
\]

We can set up the equation:

\[
m∠1 + m∠2 = 90^\circ
\]

Substituting the expressions for \(m∠1\) and \(m∠2\):

\[
(x + 2) + (x - 26) = 90
\]

Now, simplify the equation:

\[
x + 2 + x - 26 = 90
\]
\[
2x - 24 = 90
\]

Next, add \(24\) to both sides:

\[
2x = 90 + 24
\]
\[
2x = 114
\]

Now, divide by \(2\):

\[
x = 57
\]

Now that we have \(x\), we can find the measure of angle 1:

\[
m∠1 = x + 2 = 57 + 2 = 59^\circ
\]

Thus, the measure of angle 1 is

\[
\boxed{59^\circ}
\]