Three angles have measures that add to 180°. They have the following angle measures: m∠ABC=(x−6)°, m∠CBD=(4x−14)°, and m∠DBE=5x°. What is the equation to solve for x?(1 point)

Question

Responses

x°−20°=180°

10x°+20°=180°

9x°−20°=180°

10x°−20°=180°

Answer 1

The equation to solve for x is 10x°−20°=180°.

Answer 2

Two supplementary angles have the following measures: m∠ABC=135° and m∠CBD=9x°. What is the equation to solve for x?(1 point)
Responses

9x°+135°=180°
9 x plus 135 equals 180

9x°+135°=90°
9 x plus 135 equals 90

9x°=180°
9 x equals 180

9x°−135°=180°
9 x minus 135 equals 180

Answer 3

The equation to solve for x is 9x° = 180° - 135°.

Answer 4

Use facts about supplementary angles to solve the following problem. Two angles are supplementary and have measures m∠ABC=15° and m∠CBD=x°. What is the value of m∠CBD?(1 point)
Responses

165°

15°


180°

75°

Answer 5

The value of m∠CBD is 165°.

Answer 6

Question
Two angles are supplementary and have measures m∠QRS=(x+40)° and m∠SRT=x°. What is the measure of ∠QRS?(1 point)
Responses

180°

25°

110°

70°

Answer 7

The measure of ∠QRS is 180°.

Answer 8

Three angles measures add to 180° and have the following measures: m∠ACB=(x+15)° , m∠BCD=(x+48)°, and m∠DCE=13°. What is the measure of ∠BCD?(1 point)
Responses

67°

52°

80°

100°

Answer 9

To find the measure of ∠BCD, we can set up the equation:

(x+15)° + (x+48)° + 13° = 180°

Simplifying the equation gives:

2x + 76° = 180°

Subtracting 76° from both sides of the equation gives:

2x = 180° - 76°

2x = 104°

Dividing both sides by 2 gives:

x = 52°

Therefore, the measure of ∠BCD is (x+48)° = 52° + 48° = 100°.