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° 52 degrees 100° 100 degrees 80° 80 degrees 67°
Let's call the measure of ∠BCD as y.
Since three angles add up to 180°, we can write the following equation:
(x+15) + (x+48) + 13 = 180
Simplifying this equation, we get:
2x + 76 = 180
Subtracting 76 from both sides:
2x = 104
Dividing both sides by 2:
x = 52
Now, we can substitute the value of x back into the equation for the measure of ∠BCD:
y = x + 48 = 52 + 48 = 100
Therefore, the measure of ∠BCD is 100°.