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
67°
67 degrees
100°
100 degrees
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page 12 of 12
To find the measure of angle BCD, we need to set up an equation using the given information.
We know that the sum of the three angles is 180°, so we can write the equation:
(x + 15) + (x + 48) + 13 = 180
Now, let's simplify the equation:
2x + 76 = 180
Subtract 76 from both sides:
2x = 104
Divide both sides by 2:
x = 52
Now that we have the value of x, let's find the measure of angle BCD:
BCD = x + 48
BCD = 52 + 48
BCD = 100°
Therefore, the measure of angle BCD is 100 degrees.