# Two angles are complementary. The measure of the larger angle is 5 times the measure of the smaller. What are the measures of the angles?

Let ( x ) represent the measure of the smaller angle. Then, the measure of the larger angle is ( 5x ). Since the angles are complementary, their sum is ( 90^\circ ). Thus, we have the equation:

[ x + 5x = 90^\circ ]

Solving for ( x ), we get:

[ 6x = 90^\circ ]

[ x = \frac{90^\circ}{6} = 15^\circ ]

So, the measure of the smaller angle is ( 15^\circ ), and the measure of the larger angle is ( 5 \times 15^\circ = 75^\circ ).

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