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°
165 degrees
180°
180 degrees
15°
15 degrees
75°
The value of m∠CBD is 165°. This is because the measures of supplementary angles add up to 180°. Given that m∠ABC is 15°, we can subtract this from 180° to find the measure of m∠CBD: 180° - 15° = 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°
25 degrees
The measure of ∠QRS is 70°. This is because the measures of supplementary angles add up to 180°. Given that m∠SRT is x°, we can substitute this value into the equation for m∠QRS, which is (x+40)°. So, we have: x° + (x+40)° = 180°. Simplifying this equation, we get 2x + 40 = 180. Subtracting 40 from both sides, we have 2x = 140. Dividing both sides by 2, we find x = 70. Therefore, the measure of ∠QRS is 70°.
∠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
100°
100 degrees
52°
52 degrees
80°
80 degrees
128°
128 degrees
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