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)
Responses
x°−20°=180°
10x°+20°=180°
9x°−20°=180°
10x°−20°=180°
The equation to solve for x is 10x°−20°=180°.
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
The equation to solve for x is 9x° = 180° - 135°.
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°
The value of m∠CBD is 165°.
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°
The measure of ∠QRS is 180°.
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°
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°.