∠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

Complementary angles are two angles whose measures add up to \(90^\circ\). Given that \(\angle 1\) and \(\angle 2\) are complementary, we can write the equation:

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

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

\[
(x - 22) + (x - 16) = 90
\]

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

\[
x - 22 + x - 16 = 90
\]

Combine like terms:

\[
2x - 38 = 90
\]

Add 38 to both sides:

\[
2x = 128
\]

Divide by 2:

\[
x = 64
\]

Now that we have the value of \(x\), we can find the measure of \(\angle 1\) by substituting \(x\) back into the expression for \(m\angle 1\):

\[
m\angle 1 = x - 22 = 64 - 22 = 42^\circ
\]

### Answer:
The measure of \(\angle 1\) is \(42^\circ\).

Would you like more details or have any questions? Here are some related questions to explore:

1. How do you find the measure of complementary angles if one angle is given?
2. What are supplementary angles, and how are they different from complementary angles?
3. If the measure of \(\angle 1\) was given in radians, how would the calculation change?
4. How do you find the value of \(x\) if both angles are equal?
5. How would you solve this problem if you had three angles that add up to \(180^\circ\)?

**Tip:** When solving problems involving complementary or supplementary angles, always remember the key relationships: \(90^\circ\) for complementary and \(180^\circ\) for supplementary.

∠1 and ∠2 are complementary angles. If m∠1 = (x − 22)° and m∠2 = (x − 16)°, then find the measure of ∠1.

Learn how to find the measure of a complementary angle when given expressions (x − 22)° and (x − 16)°. This problem involves key concepts in algebra, including solving linear equations, and is suitable for students in Grades 7-9.

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