Question

An angle measures 84° less than the measure of its complementary angle. What is the measure of each angle?

Answer 1

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Answer 2

Answer: the two angles measure 3° and 87°

Step-by-step explanation:

Call the measure of one angle n. The other angle, which is 84° bigger, measures n + 84°.

Since the angles are complementary, their measures must add to 90°. Set up an equation and solve for n.

n+ n+ 84° = 90°

2n+  84° = 90°

2n+84° − 84° =  90° − 84°

2n= 6°

2n÷ 2 = 6° ÷ 2

n =  3°

The first angle measures 3°. Now plug in n = 3° to find the measure of the other angle, n + 84°.

n+ 84°= 3° + 84°

= 87°

So, the two angles measure 3° and 87°