Question

An angle measures 82º more than the measure of its complementary angle. What is the measure of each angle?

Answer 1

❖ Question -:

An angle measures 82º more than the measure of its complementary angle. What is the measure of each angle?

❖ Explanation -:

Given -:

• An angle measures 82º more than the measure of its complementary angle.

Need to find -:

• Measure of each angle

Assuming -:

An angle measures 82º more than the measure of its complementary angle.

Let us assume one angle as x

Then other angle = (x + 82)

Solution -:

First we will make an equation

We know,

Complementary angles add up to 90°

x + (x + 82°) = 90°

→ x + x + 82° = 90°

→ 2x + 82° = 90°

→ 2x = 90° - 82°

→ 2x = 8

→ x =
`\cancel{(8)/(2)}`

→ x = 4

Substituting the value of x = 4

One angle = x = 4°

Other angle = x + 82° = (4 + 82)° = 86°

Final Answer -:

• The angles are 4 and 86.

`\rule{180pt}{2pt}`

Answer 2

Explanation:

Let one angle be x

Other angle =x + 82

Complementary angles add up to 90

x + x + 82 = 90

2x + 82 = 90

2x = 90 - 82

2x = 8

x = 8/2

x = 4

Other angle = x + 82

= 4 +82

= 86

The angles are: 4 , 86