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
180°
180 degrees
15°
15 degrees
165°
165 degrees
75°
75 degrees
Since the two angles are supplementary, their measures add up to 180°.
m∠ABC + m∠CBD = 180°
Substituting the given values:
15° + x° = 180°
We can solve for x by subtracting 15° from both sides:
x° = 180° - 15°
x° = 165°
Therefore, the value of m∠CBD is 165°.
Solve Equations with Supplementary Angles Quick Check
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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
110°
110 degrees
25°
25 degrees
70°
70 degrees
180°
180 degrees
Since the two angles are supplementary, their measures add up to 180°.
m∠QRS + m∠SRT = 180°
Substituting the given expressions:
(x+40)° + x° = 180°
Combining like terms:
2x + 40° = 180°
Next, we can isolate the variable by subtracting 40° from both sides:
2x = 180° - 40°
2x = 140°
Finally, we can solve for x by dividing both sides by 2:
x = 140° / 2
x = 70°
Therefore, the measure of ∠QRS is (x+40)° = 70° + 40° = 110°.
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
100°
100 degrees
80°
80 degrees
52°
52 degrees
67°
The sum of the three angles is 180°:
m∠ACB + m∠BCD + m∠DCE = 180°
Substituting the given expressions:
(x+15)° + (x+48)° + 13° = 180°
Combine like terms:
2x + 76° = 180°
Next, subtract 76° from both sides to isolate the variable:
2x = 180° - 76°
2x = 104°
Finally, divide both sides by 2 to solve for x:
x = 104° / 2
x = 52°
Therefore, the measure of ∠BCD is (x+48)° = 52° + 48° = 100°.
The measure of ∠BCD is 100°.