Question

The angles represented by the expressions \left(2x+46\right)^{\circ}(2x+46) ∘ and \left(3x-6\right)^{\circ}(3x−6) ∘ are complementary angles. Find the measure of the larger angle.

Answer 1

The two complementary angles that sum up to 90° measures 24° and 66°. The larger of the two angles that are complementary measures: 66°.

What are Complementary Angles?

Complementary angles are angles that will equal 90 degrees when added together.

Given two complementary angles as:

2x + 46

3x - 6

Thus:

2x + 46 + 3x - 6 = 90

Solve for x

5x + 40 = 90

5x = 90 - 40

5x = 50

x = 10

Plug in the value of x to find the measure of each angle

2x + 46 = 2(10) + 46 = 66°

3x - 6 = 3(10) - 6 = 24°

Therefore, the larger of the two angles that are complementary measures: 66°.

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