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To find the measure of ∠BCD, we can set up the equation:
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 ∠BCD is (x+48)° = 52+48 = 100°.
The correct answer is 100 degrees.