Three angles measures add to 180°

Question

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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Answer 1

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.