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 ?

Answer 1

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

We are given that the measures of ∠ACB and ∠DCE add up to 180°, so we can use this information to find the measure of ∠BCD.

m∠ACB + m∠DCE = 180°

Substituting the given angle measures:

(x+15)° + 13° = 180°

Combining like terms:

x + 28° = 180°

Subtracting 28° from both sides:

x = 180° - 28°

x = 152°

Now that we have the value of x, we can find the measure of ∠BCD:

m∠BCD = x + 48°

Substituting the value of x:

m∠BCD = 152° + 48°

m∠BCD = 200°

Therefore, the measure of ∠BCD is 200°.