∠ACB

Question

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

Answer 1

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°.