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 100° 100 degrees 52° 52 degrees 67° 67 degrees 80°
To find the measure of ∠BCD, we need to use the fact that the sum of the angles in a triangle is 180°.
We have the following equations:
∠ACB + ∠BCD + ∠DCE = 180°
Now we can substitute 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, ∠BCD = x + 48° = 52° + 48° = 100°.
The measure of ∠BCD is 100°.