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Elementary Geometry for College St...

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

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BuyFindarrow_forward

Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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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. m1+m2=180° 2. The sum of measures of supplementary angles 1 and 2 is 180°.
3. 1 is acute 3. Given
4. Where m1=x, 0<x<90° 4. 1 is acute angle, so 0<m1<90°
5. x+m2=180° 5. Substitute x for m1 in m1+m2=90°
6. m2=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 m2 for 180°x
11. 2 is obtuse 11

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