Question

An angle measures 85.6 degrees less than of its complementary angle. What is the measure of each angle?

Answer 1

The angles are 2.2° and 87.8°

Explanation:

Let the complementary angle be 'x'.

The other angle is 85.6° less than its complementary angles.

The other angle = y

y = x - 85.6 --------------(I)

If the sum of any two angles is 90°, then they are called complementary angles.

x + y = 90

• Substitute y = x - 85.6 in the above equation,

x + (x - 85.6) = 90

x + x - 85.6 = 90

• Combine like terms. Here, x and x are like terms.

2x - 85.6 = 90

• Add 85.6 to both sides,

2x = 90 + 85.6

2x = 175.6

• Divide both sides by 2,

x = 175.6 ÷ 2

`\boxed{\bf x = 87.8^\circ}`

y = 87.8 - 85.6

= 2.2°

Answer: The angles are 2.2° and 87.8°