Question

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°

Answer 1

To find the measure of ∠BCD, we can use the fact that the sum of the angles in a triangle is 180°.

Since m∠ACB + m∠BCD + m∠DCE = 180°, we can substitute the given angle measures into 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 that we have the value of x, we can find the measure of ∠BCD by substituting x back into the equation:

m∠BCD = x + 48 = 52 + 48 = 100°

Therefore, the measure of ∠BCD is 100°.