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
52°
52 degrees
100°
100 degrees
67°
To find the measure of ∠BCD, you need to set up the equation:
(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, substitute the value of x back into the equation to find the measure of ∠BCD:
∠BCD = x + 48 = 52 + 48 = 100°
Therefore, the measure of ∠BCD is 100°.