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Math
GeometryElementary Geometry for College Students6th Edition

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Chapter 1.7, Problem 35E
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Elementary Geometry for College St...

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

Solutions

Chapter
Section
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 34E
Problem 35E
BuyFindarrow_forward

Elementary Geometry for College St...

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

In Exercises 27 to 35, complete the formal proof of each theorem.

The supplement of an acute angle is an obtuse angle.

(HINT: Use Exercise 28 of Section 1.4 as a guide.)

To determine

To find:

The complete formal proof of the given theorem.

Explanation

Given:

The given statement is,

The supplement of an acute angle is obtuse angle.

Approach:

According to the given statement of theorem, make a drawing.

Figure (1)

From figure (1), it can be observed that given and prove for theorem is,

Given: ∠1 is supplementary to ∠2 and ∠1 is actue angle.

Prove: ∠2 is obtuse.

The reasons for given statements is explained in table below.

Statements Reasons
1. ∠1 and ∠2 are supplementary 1. Given
2. m∠1+m∠2=180° 2. The sum of measures of supplementary angles ∠1 and ∠2 is 180°.
3. ∠1 is acute 3. Given
4. Where m∠1=x, 0<x<90° 4. ∠1 is acute angle, so 0<m∠1<90°
5. x+m∠2=180° 5. Substitute x for m∠1 in m∠1+m∠2=90°
6. m∠2=180°−x 6. Subtract x from both sides.
7. −x+90°<90°<180°−x 7. Substitution
8. 180°−x<180°<270°−x 8. Add 90° to each term.
9. 90°<180°−x<180° 9. If 180°−x<180°<270°−x, then 180°−x<180°
10. 90°<m/2<180° 10. Substitute m∠2 for 180°−x
11. ∠2 is obtuse 11

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