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°=180°
9 x equals 180
9x°+135°=180°
9 x plus 135 equals 180
9x°−135°=180°
9 x minus 135 equals 180
9x°+135°=90°
Solve Equations with Supplementary Angles Quick Check
1:10x°−20°=180°
2:9x°+135°=180°
3:165°
4:110°
5:100°
9x° + 135° = 180°
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
15°
15 degrees
75°
75 degrees
180°
180 degrees
165°
m∠ABC + m∠CBD = 180°
15° + x° = 180°
x = 180° - 15°
x = 165°
Therefore, the measure of ∠CBD is 165°.
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°
180 degrees
110°
110 degrees
70°
70 degrees
25°
Since two angles are supplementary, the sum of their measures is 180°.
Therefore, x + 40 + x = 180.
2x + 40 = 180.
2x = 180 - 40
2x = 140
x = 70
∠QRS = x + 40 = 70 + 40 = 110°
Therefore, the measure of ∠QRS is 110°.
∠ACB
and ∠BCD
are supplementary angles. The angles have the following measures: ∡ACB=(x+28)°
and ∡BCD=(x+48)°
. What is m∠BCD
?(1 point)
Responses
128°
128 degrees
52°
52 degrees
100°
100 degrees
80°
Since ∠ACB and ∠BCD are supplementary angles, their measures sum up to 180°.
Therefore, (x + 28) + (x + 48) = 180
2x + 76 = 180
2x = 180 - 76
2x = 104
x = 52
Therefore, the measure of ∠BCD is x + 48 = 52 + 48 = 100°.
So, the measure of ∠BCD is 100°.
To solve equations with supplementary angles, you apply the property that the sum of two supplementary angles is 180 degrees.
1. 10x° - 20° = 180°
Add 20° to both sides: 10x° = 200°
Divide by 10: x = 20°
2. 9x° + 135° = 180°
Subtract 135° from both sides: 9x° = 45°
Divide by 9: x = 5°
Therefore, the solutions are:
1: x = 20°
2: x = 5°
So, none of the options listed (3, 4, 5) are the solutions to the given equations.