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

Answer:

 - 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.

Step-by-step 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:

$If\ a=b,\ then\ \frac{a}{c}=\frac{b}{c}$

- 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   $m\angle B=-6x-39$)