   Chapter 1.6, Problem 28E ### Elementary Geometry for College St...

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

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

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

# In the proof below, provide the missing reasons. Given: ∠ 1 and ∠ 2 are complementary ∠ 1 is acute Prove: ∠ 2 is also acute PROOF Statements Reasons 1. ∠ 1 and ∠ 2 are complementary 1. ? (1) 2. m ∠ 1 + m ∠ 2 = 90 2. ? 3. ∠ 1 is acute 3. ? (3) 4. Where m ∠ 1 = x , 0 < x < 90 4. ? (2) 5. x + m ∠ 2 = 90 5. ? (5) 6. m ∠ 2 = 90 − x 6. ? (4) 7. − x < 0 < 90 − x 7. ? (7) 8. 90 − x < 90 < 180 − x 8. ? (7), (8) 9. 0 < 90 − x < 90 9. ? (6), (9) 10. 0 < m / 2 < 90 10. ? (10) 11. ∠ 2 is acute 11. ?

To determine

To state:

The reasons for given statements.

Explanation

Given:

Two complementary angles 1 and 2. Angle 2 is acute angle.

Approach:

If the sum of two angles is 90° then the angles are known as complementary angles.

Calculation:

The reasons for given statements is explained in table below.

 Statements Reasons 1. ∠1 and ∠2 are complementary 1. Given 2. m∠1+m∠2=90° 2. The sum of measures of complementary angles ∠1 and ∠2 is 90°. 3. ∠1 is acute 3. Given 4. Where m∠1=x, 0

Table 1

Conclusion:

The reasons for given statement is shown in Table 1

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