Question

∠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°

Answer 1

To find the measure of angle BCD given that angles ACB and BCD are supplementary, we can set up the equation based on the information provided.

Given:
- m∠ACB = (x + 28)°
- m∠BCD = (x + 48)°

Since the angles are supplementary, we have:

m∠ACB + m∠BCD = 180°

Substituting the expressions for the angles:

(x + 28) + (x + 48) = 180

Combining like terms:

2x + 76 = 180

Now, subtract 76 from both sides:

2x = 180 - 76
2x = 104

Now, divide by 2:

x = 52

Now that we have x, we can find the measure of angle BCD:

m∠BCD = x + 48
m∠BCD = 52 + 48
m∠BCD = 100°

Therefore, the measure of angle BCD is **100°**.