Three angles measures add to 180°%0D%0A180%0D%0A°%0D%0A and have the following measures: m∠ACB=(x+15)°%0D%0A%0D%0A∠%0D%0A%0D%0A%0D%0A%0D%0A=%0D%0A(%0D%0A%0D%0A+%0D%0A15%0D%0A)%0D%0A°%0D%0A , m∠BCD=(x+48)°%0D%0A%0D%0A∠%0D%0A%0D%0A%0D%0A%0D%0A=%0D%0A(%0D%0A%0D%0A+%0D%0A48%0D%0A)%0D%0A°%0D%0A , and m∠DCE=13°%0D%0A%0D%0A∠%0D%0A%0D%0A%0D%0A%0D%0A=%0D%0A13%0D%0A°%0D%0A . What is the measure of ∠BCD%0D%0A∠%0D%0A%0D%0A%0D%0A%0D%0A ?(1 point)%0D%0AResponses%0D%0A%0D%0A67°%0D%0A67%0D%0A°%0D%0A 67 degrees%0D%0A%0D%0A52°%0D%0A52%0D%0A°%0D%0A 52 degrees%0D%0A%0D%0A100°%0D%0A100%0D%0A°%0D%0A100 degrees%0D%0A%0D%0A80°
To find the measure of angle BCD, we can use the fact that the sum of the three angles is 180°.
m∠ACB + m∠BCD + m∠DCE = 180°
Substituting the given angle measures:
(x+15)° + (x+48)° + 13° = 180°
Combining like terms:
2x + 76 = 180
Subtracting 76 from both sides:
2x = 104
Dividing both sides by 2:
x = 52
Therefore, the measure of angle BCD is:
m∠BCD = x + 48 = 52 + 48 = 100°
So, the answer is 100 degrees.