Question

Given: ∠A and ∠B are complementary angles. m∠A=3x+105 ; m∠B=−6x−39 Prove: m∠B=9° Drag and drop reasons into the boxes to correctly complete the proof. Statement Reason

∠A and ∠B are complementary angles. Given
m∠A=3x+105 ; m∠B=−6x−39 Given
m∠A+m∠B=90° Definition of complementary angles
3x+105−6x−39=90 Substitution Property of Equality
−3x+105−39=90 Simplify.
−3x+66=90 Simplify.
−3x=24
 x=−8
 m∠B=−6(−8)−39
 m∠B=48−39 Simplify.
m∠B=9°

Answer 1

Given:
`\angle A` and
`\angle B` are complementary angles.

`m \angle A = 3x+105^\circ` and
`m \angle B = -6x-39^\circ`.

To prove:
`m \angle B = 9^\circ`

Proof:

Statement 1:
`\angle A` and
`\angle B` are complementary angles.

Reason 1: Given

Statement 2:
`m \angle A = 3x+105^\circ` and
`m \angle B = -6x-39^\circ`.

Reason 2: Given

Statement 3:
`m \angle A + m \angle B = 90^\circ`

Reason 3: Definition of complementary angles.

Statement 4:
`3x+105^\circ -6x -39^\circ = 90^\circ`

Reason 4: Substitution property of equality

Statement 5:
`-3x+105^\circ-39^\circ = 90^\circ`

Reason 5: Simplification

Statement 6:
`-3x+66^\circ = 90^\circ`

Reason 6: Simplification

Statement 7:
`-3x = 24^\circ`

Reason 7: Simplification

Statement 8:
`x = -8`

Reason 8: Multiplication property of equality

Statement 9:
`m \angle B = -6(-8) - 39^\circ`

Reason 9: Substituting the value of 'x'

Statement 10:
`m \angle B = 48-39 = 9^\circ`

Reason 10: Simplification

Answer 2

Statement: -3x=90-66

Reason: By subtraction property of equality..

Statement: -3x=24

Reason: By simplification.

Statement: x=
`(24)/(-3)`

Reason: By division property of equality.

Statement:
`m\angle B= -6(-8)-39`

Reason: By substitution property of equality.

Statement:
`m\angle B=9^(\circ)`

Reason: By simplification.

Explanation:

Given
`\angle A` and
`\angle B` are complementary angles.

`m\angle A= 3x+105`

`m\angle B=-6x-39`

To prove that
`m\angle B=9^(\circ)`

Proof:

1.Statement:
`\angle A\; and\; \angle B` are complementary angles .

Reason: Given .

2.Statement:
`m\angle A=3x+105`;
`m\angle B= -6x-39`

Reason: Given .

3. Statement:
`m\angle A+ m\angle B=90^(\circ)`

Reason: By definition of complementary angles.

4.Statement:
`3x+105-6x-39=90`

Reason: By substitution property of equality.

5. Statement:
`-3x+105-39=90`

Reason: By simplification.

6. Statement:
`-3x+66=90`

Reason: By simplification.

7. Statement:
`-3x= 90-66`

Reason: By subtraction property of equality .

8.Statement:
`-3x=24`

Reason: By simplification.

9.Statement:
`x=(24)/(-3)`

Reason : By division property of equality.

10. Statement: x=-8

Reason: By simplification.

11. Statement:
`m\angle B= -6(-8)-39`

Reason : By substitution property of equality.

12. Statement:
`m\angle B= 48-39`

Reason: By simplification.

13. Statement:
`m\angle B=9^(\circ)`

Reason : By simplification.

Hence,
`m\angle B= 9^(\circ)`

Hence proved.