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.

 - For the statement , the reason is: Subtraction property of Equality

- For the statement , the reason is: Division property of Equality.

- For the statement , 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:

- The Division property of Equality states that:

- The Substitution property of Equality states that:

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

 - For the statement , the reason is:

Subtraction property of Equality

(Because it is obtained by subtracting  66 from both sides of )

- For the statement , the reason is:

Division property of Equality

(Because it is obtained by dividing both sides of   by -3)

- For the statement , the reason is:

Substitution property of Equality

(Because it is obtained by substituting the value of "x" into   )

3+x

step-by-step explanation: