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?
80° 80 degrees 67° 67 degrees 52° 52 degrees
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.