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
80°
80 degrees
100°
100 degrees
67°
67 degrees
52°
To solve this problem, we can use the fact that the sum of the measures of the three angles is equal to 180°.
Therefore, we can set up the equation:
(x+15) + (x+48) + 13 = 180
Combining like terms, we get:
2x + 76 = 180
Subtracting 76 from both sides, we get:
2x = 104
Dividing both sides by 2, we get:
x = 52
Therefore, the measure of angle BCD is x + 48 = 52 + 48 = 100°.
So the correct answer is 100°.