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)
We know that the sum of angles in a triangle is 180°. Therefore, we can write the equation:
∠B + ∠C + ∠D = 180°
Substituting the given measures, we have:
25° + 3x° + (3x + 5)° = 180°
Now we can solve for x:
25° + 3x° + 3x° + 5° = 180°
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:
∠C = 3x = 3(25°) = 75°
∠D = 3x + 5 = 3(25°) + 5° = 75° + 5° = 80°
Therefore, the measure of ∠C is 75° and the measure of ∠D is 80°.