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?
A. 52
B. 100
C. 67
D. 80
Since the three angles ACB, BCD, and DCE add up to 180 degrees, we can write the equation:
(x + 15) + (x + 48) + 13 = 180
Combining like terms, we get:
2x + 76 = 180
Subtracting 76 from both sides, we have:
2x = 104
Finally, dividing both sides by 2, we find:
x = 52
Therefore, the measure of BCD is:
x + 48 = 52 + 48 = 100
The answer is B. 100.