Question

Angle e and angle f are complementary. The measure of angle e is 54 degrees more than the measure of angle f. Find the measure of each angle.

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1. Given that \( e \) and \( f \) are complementary, we know

e + f = 90^\circ

2. We are told that \( e \) is 54 degrees more than \( f \), so

e = f + 54^\circ

3. Substitute the second equation into the first equation:

(f + 54^\circ) + f = 90^\circ

4. Combine like terms:

2f + 54^\circ = 90^\circ

5. Subtract 54 degrees from both sides:

2f = 36^\circ

6. Divide by 2:

f = 18^\circ

7. Now, substitute \( f = 18^\circ \) back into the equation \( e = f + 54^\circ \):

e = 18^\circ + 54^\circ

e = 72^\circ

Therefore, the measures of the angles are:

e = 72^\circ, \, f = 18^\circ

2. We are told that \( e \) is 54 degrees more than \( f \), so

3. Substitute the second equation into the first equation:

4. Combine like terms:

5. Subtract 54 degrees from both sides:

6. Divide by 2:

7. Now, substitute \( f = 18^\circ \) back into the equation \( e = f + 54^\circ \):

Therefore, the measures of the angles are:

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