Question

The measure of an angle is nine times the measure of its complement. Find the measure of each angle.

The smaller angle measures
The larger angle measures.

Answer 1

The measure of the smaller angle is 81 degrees and the larger angle measures 81 degrees.

Step-by-step explanation:

Let the measure of the smaller angle be x degrees. The measure of its complement will be (90 - x) degrees. According to the given condition, the measure of the angle is nine times the measure of its complement, so we have the equation:

x = 9(90 - x)

Simplifying the equation, we get:

10x = 810

x = 81

Therefore, the smaller angle measures 81 degrees and the larger angle measures 9(90 - 81) = 9(9) = 81 degrees.

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