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An angle measures 152° less than the measure of its supplementary angle. What is the measure of each angle?

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musiclover10045

Two supplementary angles when added together need to equal 180 degrees.

Let the first angle = X

The second angle would then be X - 152

Add them together to equal 180:

X + X - 152 = 180

Simplify:

2X -152 = 180

Add 152 to each side:

2X = 332

Divide both sides by 2:

X = 332 / 2

X = 166

The first angle = X = 166 degrees.

The second angle = X - 152 = 166 - 152 = 14 degrees.

The angles are 166 and 14

anuksha0456

The measure of each angle = 166°, 14°

What do we mean by supplementary angles?

Supplementary angles are defined by a pair of angles which when added, gives a result of 180°.

How do we solve the given question?

Let the greater angle in the pair be X = x°.

∴ The smaller angle = 180° - x°.

By question, the difference between the greater and the smaller angle = 152°.

⇒ x° - (180° - x°) = 152°

⇒ x° - 180° + x° = 152°

⇒ 2x° = 152° + 180°

⇒ 2x° = 332°

⇒ x° = 332°/2 = 166°

∴ The greater angle = 166°.

The smaller angle = 180° - 166° = 14°.

The measure of each angle = 166°, 14°

Learn more about Supplementary Angles at

https://brainly.com/question/2046046

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