Question

Given: ∠A and ∠B are complementary angles.

m∠A=3x+105 ; m∠B=−6x−39

Prove: m∠B=9°

1. 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° Simplify.

Answer 1

- For the statement
`-3x=24`, the reason is: Subtraction property of Equality

- For the statement
`x=-8`, the reason is: Division property of Equality.

- For the statement
`m\angle B=-6(-8)-39`, the reason is: Substitution property of Equality.

Explanation:

The missing pictures are attached.

We must remember that:

- The Subtraction property of Equality states that:

`If\ a=b,\ then\ a+c=b+c`

- The Division property of Equality states that:

`If\ a=b,\ then\ (a)/(c)=(b)/(c)`

- The Substitution property of Equality states that:

`If\ a=b,\ then\ b\ can\ replace\ a`

Knowing this properties we can identify the missing reasons that correctly complete the proof.

- For the statement
`-3x=24`, the reason is:

Subtraction property of Equality

(Because it is obtained by subtracting 66 from both sides of
`-3x+66=90`)

- For the statement
`x=-8`, the reason is:

Division property of Equality

(Because it is obtained by dividing both sides of
`-3x=24` by -3)

- For the statement
`m\angle B=-6(-8)-39`, the reason is:

Substitution property of Equality

(Because it is obtained by substituting the value of "x" into
`m\angle B=-6x-39`)