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) Responses 52° 52 degrees 67° 67 degrees 100° 100 degrees 80° 80 degrees
To find the measure of ∠BCD, we can set up an equation using the property that the sum of the angles in a triangle is 180°.
m∠ACB + m∠BCD + m∠DCE = 180°
Substituting the given angle measures:
(x+15)° + (x+48)° + 13° = 180°
Simplifying:
2x + 76° = 180°
Subtracting 76° from both sides:
2x = 104°
Dividing both sides by 2:
x = 52°
Therefore, the measure of ∠BCD is (x+48)° = 52° + 48° = 100°.
The answer is 100°.