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 67° 67 degrees 52° 52 degrees 100°

Answer 1

Let's set up an equation using the fact that the sum of the three angles 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

Now we can find the measure of ∠BCD by plugging in x = 52:

∠BCD = x + 48 = 52 + 48 = 100°

Therefore, the measure of ∠BCD is 100°.