Three angles measures add to 180°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)Responses100°100 degrees52° 52 degrees67° 67 degrees80°
To find the measure of ∠BCD, we need to set up an equation using the fact that the sum of the three angles is 180 degrees.
m∠ACB + m∠BCD + m∠DCE = 180
Substituting the given angle measures:
(x + 15) + (x + 48) + 13 = 180
Simplifying the equation:
2x + 76 = 180
2x = 104
x = 52
Now we can find the measure of ∠BCD using x:
m∠BCD = x + 48 = 52 + 48 = 100°
Therefore, the measure of ∠BCD is 100 degrees.