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°

Statement: -3x=90-66

Reason: By subtraction property of equality..

Statement: -3x=24

Reason: By simplification.

Statement: x=

Reason: By division property of equality.

Statement:

Reason: By substitution property of equality.

Statement:

Reason: By simplification.

Step-by-step explanation:

Given and are complementary angles.

To prove that

Proof:

1.Statement: are complementary angles .

Reason: Given .

2.Statement:  ;

Reason: Given .

3. Statement:

Reason: By definition of complementary angles.

4.Statement:

Reason: By substitution  property of equality.

5. Statement:

Reason: By simplification.

6. Statement:  

Reason: By simplification.

7. Statement:

Reason: By subtraction property of equality .

8.Statement:

Reason: By simplification.

9.Statement:

Reason : By division property of equality.

10. Statement: x=-8

Reason: By simplification.

11. Statement:

Reason : By substitution property of equality.

12. Statement:

Reason: By simplification.

13. Statement:

Reason : By simplification.

Hence,

Hence proved.

complete the steps to find the area of the trapezoid.

area of rectangle = 256   square units

area of triangle 1 = 24  square units

area of triangle 2 = 16  square units

area of triangle 3 =   96 square units

area of trapezoid = 120  square units

step-by-step explanation: