Question

The difference of two complementary angles is 17 degrees. Find the measures of the angles.

Answer 1

The measurement of both angles are 36.5° and 53.5°

Step-by-step explanation:

Let x be one angle then the other angle will be 90-x

According to the given statement

The difference of two complementary angles is 17 degrees

$90-x-x = 17\\90-2x = 17\\-2x = 17-90\\-2x = -73$

Dividing both sides by -2

$\frac{-2x}{-2} = \frac{-73}{-2}\\x = 36.5$

The second angle will be:

$90-x\\=90-36.5\\=53.5$

The measurement of both angles are 36.5° and 53.5°

Keywords: angles, Complementary Angles

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Answer 2

The measures of the angles: 36.5 and 53.5

Further explanation

One variable linear equation is an equation that has a variable and the exponent number is one.

Can be stated in the form:

$\large {\boxed {\bold {ax = b}}$

or

ax + b = c, where a, b, and c are constants, x is a variable

There are two angles that can form:

• Supplementary Angles: if both angles are added = 180 °
• Complementary Angles: if both angles are added = 90 °

The difference of two complementary angles is 17 degrees

Let angle 1 = x, angle 2 = 90-x

We express it in the form of algebraic equations

(90-x) - x = 17

90 - 2x = 17

90-17 = 2x

73 = 2x

x = 36.5 (angle 1)

angle 2 = 90 -x

angle 2 = 90- 36.5

angle 2 = 53.5

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