Question

An angle measures 15 degrees more than its complement. Find the measures of the two angles

Answer 1

The first angle is 37.5° and the second would be 52.5°

Explanation:

Angles are complementary when their sums add up to 90°.

`x+(x+15) = 90\\x+x+15=90\\x+x=75\\x=37.5`

The first angle is 37.5° and the second would be 52.5°, after we plug in x.

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Answer 2

• Angle 1 = x = 37.5°
• Angle 2 = x + 15 = 52.5°

Concept:

Here, we need to know the idea of the complementary angle.

Two angles are said to be complementary if they add up to 90 degrees.

Be aware that three or more angles cannot be complementary even if their sum is 90 degrees.

Solve:

Given information

Angle 1 = x

Angle 2 = x + 15

Given expression deducted from the definition of the complementary angle

Angle 1 + Angle 2 = 90

Substitute values into the expression

(x) + (x + 15) = 90

Combine like terms

(x + x) + 15 = 90

2x + 15 = 90

Subtract 15 on both sides

2x + 15 - 15 = 90 - 15

2x = 75

Divide 2 on both sides

2x / x = 75 / 2

`\boxed{x=37.5}`

Find the measure of angle 2

Angle 2 = x + 15 ⇔ Given expression

Angle 2 = (37.5) + 15 ⇔ Substitute values into the expression

Angle 2 =
`\boxed{52.5}` ⇔ Simplify by addition

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