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 ?

Question

Responses:
100°
80°
67°
52°

Answer 1

To find the measure of ∠BCD, we can use the fact that the sum of the angle measures in a triangle is 180°.

We have m∠ACB = (x+15)°, m∠BCD = (x+48)°, and m∠DCE = 13°.

So, (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 ∠BCD is x + 48 = 52 + 48 = 100°.

So, the correct answer is 100°.