∠ACB and ∠BCD are supplementary angles. The angles have the following measures: ∡ACB=(x+28)° and ∡BCD=(x+48)° . What is m∠BCD ?(1
Since ∠ACB and ∠BCD are supplementary angles, their measures add up to 180 degrees.
So, (x+28) + (x+48) = 180.
Combining like terms, 2x + 76 = 180.
Subtracting 76 from both sides, 2x = 104.
Dividing by 2, x = 52.
Therefore, ∠BCD = (x+48) = 52 + 48 = 100.
The measure of ∠BCD is 100 degrees.