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

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

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

**Final answer:**
- \( m\angle F = 18^\circ \)
- \( m\angle E = 72^\circ \)

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!

∠E and ∠F are complementary. The measure of ∠E is 54° more than the measure of ∠F. Find the measure of each angle.

Learn how to find the measures of two complementary angles where the larger angle is 54° more than the smaller. Step-by-step algebraic solution involving complementary angles and equations, suitable for students in Grades 6-8.

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