∠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
128°
128 degrees
80°
80 degrees
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page 12 of 12
To find the measure of angle BCD, we need to use the fact that supplementary angles add up to 180 degrees.
We have ∠ACB = (x+28)° and ∠BCD = (x+48)°.
Since ∠ACB and ∠BCD are supplementary, we have the equation:
∠ACB + ∠BCD = 180°
Substituting the given measures, we get:
(x+28) + (x+48) = 180
Simplifying the equation, we get:
2x + 76 = 180
Subtracting 76 from both sides, we get:
2x = 104
Dividing both sides by 2, we get:
x = 52
Therefore, m∠BCD = (x+48)° = 52+48 = 100°.
So the correct answer is:
m∠BCD = 100°.