Math Problem Statement
∠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
Solution
Complementary angles are two angles whose measures add up to . Given that and are complementary, we can write the equation:
Substituting the given expressions for and :
Now, let's solve for :
Combine like terms:
Add 38 to both sides:
Divide by 2:
Now that we have the value of , we can find the measure of by substituting back into the expression for :
Answer:
The measure of is .
Would you like more details or have any questions? Here are some related questions to explore:
- How do you find the measure of complementary angles if one angle is given?
- What are supplementary angles, and how are they different from complementary angles?
- If the measure of was given in radians, how would the calculation change?
- How do you find the value of if both angles are equal?
- How would you solve this problem if you had three angles that add up to ?
Tip: When solving problems involving complementary or supplementary angles, always remember the key relationships: for complementary and for supplementary.
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Math Problem Analysis
Mathematical Concepts
Complementary Angles
Linear Equations
Formulas
m∠1 + m∠2 = 90°
Solving linear equations
Theorems
Complementary Angle Theorem
Suitable Grade Level
Grades 7-9