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°
Let's solve for the measure of ∠BCD.
We know that the sum of the three angles is 180°, so we can set up the following equation:
∠ACB + ∠BCD + ∠DCE = 180°
Substituting the given angle measures:
(x+15) + (x+48) + 13 = 180
Simplifying the equation:
2x + 76 = 180
Subtracting 76 from both sides:
2x = 104
Dividing both sides by 2:
x = 52
Therefore, the measure of ∠BCD is:
∠BCD = x + 48 = 52 + 48 = 100°