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
52°
52 degrees
100°
100 degrees
67°
67 degrees
80°
To find the measure of ∠BCD, we need to set up an equation.
Since the sum of the three angles is 180 degrees, we can write:
(x+15) + (x+48) + 13 = 180
Combining like terms, we get:
2x + 76 = 180
Subtracting 76 from both sides, we have:
2x = 104
Dividing both sides by 2, we get:
x = 52
Therefore, the measure of ∠BCD is x+48 = 52+48 = 100°.
The correct answer is 100 degrees.