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 xx degrees.
  • The measure of ∠E is then x+54x + 54^\circ, since ∠E is 54° more than ∠F.

Since the angles are complementary, their sum is 90°: x+(x+54)=90x + (x + 54^\circ) = 90^\circ Simplifying: 2x+54=902x + 54^\circ = 90^\circ Subtract 54° from both sides: 2x=362x = 36^\circ Divide by 2: x=18x = 18^\circ

Thus, the measure of ∠F is 1818^\circ and the measure of ∠E is: x+54=18+54=72x + 54^\circ = 18^\circ + 54^\circ = 72^\circ

Final answer:

  • mF=18m\angle F = 18^\circ
  • mE=72m\angle E = 72^\circ

Would you like further details or explanations?

Here are some related questions:

  1. What happens if the angles are supplementary instead of complementary?
  2. How do you determine the measure of an angle if it's described as a certain degree less than another?
  3. What is the process for solving problems involving supplementary angles?
  4. How would you solve a problem where the sum of two angles is 180°?
  5. 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