∠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

80°
80 degrees

52°
52 degrees

128°

1 answer

To find the measure of ∠BCD, we can use the fact that supplementary angles add up to 180 degrees.

So, we have:
∠ACB + ∠BCD = 180°

And we know that:
∠ACB = (x+28)°
∠BCD = (x+48)°

Substituting these values into the equation, 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, the measure of ∠BCD is:
∠BCD = x + 48 = 52 + 48 = 100°

Therefore, the correct answer is 100 degrees.