Question

Two angles are complementary.The larger angle is 30 degrees more than 4 times the smaller

angle find the measure of each angle
Define variables

Answer 1

Explanation:

Remark

2 angles are complementary means that 2 angles add up to 90°. That is the guiding princeple behind the problem.

Givens

Let the smallest angle = x

Let the largest angle = 4x + 30

Equation

4x + 30° + x = 90° Combine like terms on the left

Solution

5x + 30 = 90 Subtract 30 from both sides.

5x + 30 - 30 = 90 - 30 Combine

5x = 60 Divide both sides by 5

5x/5 = 60/5

x = 12

Answer

• smallest angle = 12
• Larger angle = 4*12 + 30 = 78