Question
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 measures of ∠C and ∠D, we can use the fact that the sum of the angles in a triangle is 180°.
m∠B + m∠C + m∠D = 180°
Substituting the given values:
25° + (3x)° + (3x + 5)° = 180°
Combining like terms:
25° + 6x° + 5° = 180°
Simplifying:
30° + 6x° = 180°
Subtracting 30° from both sides:
6x° = 150°
Dividing both sides by 6:
x° = 25°
Now we can substitute this value of x back into the original equations to find the measures of ∠C and ∠D.
m∠C = 3x°
m∠C = 3(25°)
m∠C = 75°
m∠D = 3x + 5°
m∠D = 3(25°) + 5°
m∠D = 75° + 5°
m∠D = 80°
Therefore, the measures of ∠C are 75° and ∠D are 80°.