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 | 10. ? | |
(10) 11. ∠2 is acute | 11. ? |
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