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?
Since the three angles add up to 180°, we can write the equation:
(x+15) + (x+48) + 13 = 180
Combining like terms:
2x + 76 = 180
Subtracting 76 from both sides:
2x = 104
Dividing both sides by 2:
x = 52
Now we can find the measure of ∠BCD:
m∠BCD = x + 48 = 52 + 48 = <<52+48=100>>100°
So, the measure of ∠BCD is 100°.