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=
°
Since together, the measures of ∠B, ∠C, and ∠D equal 180°, we can write the equation:
m∠B + m∠C + m∠D = 180°
Substituting the given values, we get:
25° + 3x° + (3x + 5)° = 180°
Combining the like terms:
25° + 6x° + 5° = 180°
Simplifying, we have:
6x° + 30° = 180°
Subtracting 30° from both sides:
6x° = 150°
Dividing both sides by 6:
x° = 25°
Now, we can find the measures of ∠C and ∠D:
m∠C = 3x° = 3(25°) = 75°
m∠D = 3x + 5° = 3(25°) + 5° = 75° + 5° = 80°
Therefore, the measures of ∠C and ∠D are:
m∠C = 75°
m∠D = 80°