Together, the measures of ∠B , ∠C , and ∠D equal 180° . The angles have the following measures: m∠B=25° , m∠C=(3x)° , and m∠D=(3x+5)° . What are the measures of ∠C and ∠D ?(1 point)
m∠C=__°
m∠D=__°
To find the measure of ∠C, we can use the information that the sum of ∠B, ∠C, and ∠D equals 180°.
∠B + ∠C + ∠D = 180°
Substituting the given measures, we have:
25° + 3x° + (3x+5)° = 180°
Combine like terms:
25° + 6x° + 5° = 180°
Combine constant terms:
30° + 6x° = 180°
Subtract 30° from both sides:
6x° = 150°
Divide both sides by 6:
x° = 25°
Now that we have the value of x, we can find the measure of ∠C:
m∠C = 3x° = 3(25°) = 75°
And the measure of ∠D:
m∠D = 3x+5° = 3(25°)+5° = 75°+5° = 80°
Therefore, the measures of ∠C and ∠D are 75° and 80°, respectively.