Question
∠1 and angle, 2∠2 are complementary angles. If m, angle, 1, equals, left parenthesis, x, minus, 22, right parenthesis, degreesm∠1=(x−22)
∘
and m, angle, 2, equals, left parenthesis, x, minus, 16, right parenthesis, degreesm∠2=(x−16)
∘
, then find the measure of angle, 1∠1.
∘
and m, angle, 2, equals, left parenthesis, x, minus, 16, right parenthesis, degreesm∠2=(x−16)
∘
, then find the measure of angle, 1∠1.
Answers
GPT-4o mini
To find the measure of angle \( \angle 1 \), we know from the problem that \( \angle 1 \) and \( \angle 2 \) are complementary angles. This means that:
\[
m\angle 1 + m\angle 2 = 90^\circ
\]
Given that:
\[
m\angle 1 = (x - 22)^\circ
\]
and
\[
m\angle 2 = (x - 16)^\circ
\]
we can substitute these expressions into the equation for complementary angles:
\[
(x - 22) + (x - 16) = 90
\]
Now, combine like terms:
\[
2x - 38 = 90
\]
Next, add 38 to both sides:
\[
2x = 128
\]
Now, divide by 2:
\[
x = 64
\]
Now that we have the value of \( x \), we can find \( m\angle 1 \):
\[
m\angle 1 = x - 22 = 64 - 22 = 42^\circ
\]
Therefore, the measure of angle \( \angle 1 \) is
\[
\boxed{42^\circ}
\]
\[
m\angle 1 + m\angle 2 = 90^\circ
\]
Given that:
\[
m\angle 1 = (x - 22)^\circ
\]
and
\[
m\angle 2 = (x - 16)^\circ
\]
we can substitute these expressions into the equation for complementary angles:
\[
(x - 22) + (x - 16) = 90
\]
Now, combine like terms:
\[
2x - 38 = 90
\]
Next, add 38 to both sides:
\[
2x = 128
\]
Now, divide by 2:
\[
x = 64
\]
Now that we have the value of \( x \), we can find \( m\angle 1 \):
\[
m\angle 1 = x - 22 = 64 - 22 = 42^\circ
\]
Therefore, the measure of angle \( \angle 1 \) is
\[
\boxed{42^\circ}
\]