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 52° 52 degrees 80° 80 degrees 67° 67 degrees 100° 100 degrees
To find the measure of angle BCD, we need to set up an equation. Since the sum of the three angles is equal to 180°, we have:
(x+15) + (x+48) + 13 = 180
Combining like terms, we have:
2x + 76 = 180
Subtracting 76 from both sides, we get:
2x = 104
Dividing by 2, we find:
x = 52
Therefore, the measure of angle BCD is:
x + 48 = 52 + 48 = 100°
So the correct answer is 100°.