Question

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

100°
100 degrees

67°
67 degrees

80°
80 degrees

52°

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the measure of ∠BCD, we can set up an equation using the fact that the sum of the angle measures in a triangle is 180°.

(x + 15) + (x + 48) + 13 = 180

Combine like terms:

2x + 76 = 180

Subtract 76 from both sides:

2x = 104

Divide both sides by 2:

x = 52

The measure of ∠BCD is (x + 48)°, so substituting x = 52, we get:

∠BCD = 52 + 48 = 100°

Therefore, the measure of ∠BCD is 100 degrees.