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Math
GeometryElementary Geometry for College Students6th Edition

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Chapter 1.CR, Problem 37CR
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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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State whether the sentences in Review Exercises 33 to 37 are always true (A), sometimes true (S), or never true (N).

The supplement of an obtuse angle is another obtuse angle.

To determine

To check:

The given statement is always true (A), sometimes true (S), or never true (N).

Explanation

Given:

The given statement is,

The supplement of an obtuse angle is another obtuse angle.

Definition:

If the measure of an angle is more than 90° and less than 180°, then that angle is known as obtuse angle.

If the sum of two angles is 180°, then the angles are known as supplementary angles. Each angle in the pair is the supplement of the other angle.

Approach:

Let the two angles be ∠1 and ∠2. It is given that one of the angles is an obtuse angle. Let ∠1 be the obtuse angle. It means that,

90°<m∠1<180°…(1)

According to supplement angle,

m∠1+m∠2=180°m∠2=180°−m∠1

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