Math Problem Statement
∠E and ∠F are complementary. The measure of ∠E is 54° more than the measure of ∠F. Find the measure of each angle.
Solution
The problem states that angles ∠E and ∠F are complementary, meaning their measures add up to 90°. Additionally, the measure of ∠E is 54° more than the measure of ∠F.
Let's define the measures of the angles:
- Let the measure of ∠F be degrees.
- The measure of ∠E is then , since ∠E is 54° more than ∠F.
Since the angles are complementary, their sum is 90°: Simplifying: Subtract 54° from both sides: Divide by 2:
Thus, the measure of ∠F is and the measure of ∠E is:
Final answer:
Would you like further details or explanations?
Here are some related questions:
- What happens if the angles are supplementary instead of complementary?
- How do you determine the measure of an angle if it's described as a certain degree less than another?
- What is the process for solving problems involving supplementary angles?
- How would you solve a problem where the sum of two angles is 180°?
- Can you explain why the sum of complementary angles is always 90°?
Tip: Always check if angles are complementary or supplementary before setting up your equation!
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Math Problem Analysis
Mathematical Concepts
Algebra
Complementary Angles
Basic Equations
Formulas
x + (x + 54°) = 90°
Theorems
Complementary Angles Theorem
Suitable Grade Level
Grade 6-8