Three angles measures add to 180° and have the following measures: m∠ACB=(x+15)° , m∠BCD=(x+48)° , and m∠DCE=13° . What is the measure of ∠BCD ?(1 point) Responses 80° 80 degrees 67° 67 degrees 52° 52 degrees 100°
Let's set up an equation using the fact that the sum of the three angles is 180°.
(x+15) + (x+48) + 13 = 180
Combine like terms:
2x + 76 = 180
Subtract 76 from both sides:
2x = 104
Divide both sides by 2:
x = 52
Now we can find the measure of ∠BCD by plugging in x = 52:
∠BCD = x + 48 = 52 + 48 = 100°
Therefore, the measure of ∠BCD is 100°.