Question

∠e and ∠f are complementary. the measure of ∠e is 54° more than the measure of ∠f. find the measure of each angle. m∠f = 14, m∠e = 36 (incorrect attempt shown, 2 tries left, need help options)

Explanation:

Step1: Define variables

Let \( m\angle F = x \). Then \( m\angle E = x + 54^\circ \) (since \( \angle E \) is \( 54^\circ \) more than \( \angle F \)).

Step2: Use complementary angles property

Complementary angles sum to \( 90^\circ \), so \( m\angle E + m\angle F = 90^\circ \). Substitute the expressions:
\( (x + 54^\circ) + x = 90^\circ \)

Step3: Solve for \( x \)

Combine like terms: \( 2x + 54^\circ = 90^\circ \)
Subtract \( 54^\circ \) from both sides: \( 2x = 90^\circ - 54^\circ = 36^\circ \)
Divide by 2: \( x = \frac{36^\circ}{2} = 18^\circ \)

Step4: Find \( m\angle E \)

\( m\angle E = x + 54^\circ = 18^\circ + 54^\circ = 72^\circ \)

Answer:

\( m\angle F = 18^\circ \), \( m\angle E = 72^\circ \)