∠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
80°
80 degrees
128°
128 degrees
100°
100 degrees
52°
m∠BCD = 180° - m∠ACB
m∠BCD = 180° - (x + 28)° = 180° - x - 28° = 152° - x°
Given that m∠BCD = x + 48°, we can set up the equation:
152° - x = x + 48
152° = 2x + 48
2x = 152 - 48
2x = 104
x = 52
Therefore, m∠BCD = x + 48 = 52 + 48 = 100°
Therefore, the answer is:
100°