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=°
To find the measure of ∠C, we can use the fact that the sum of the angles in a triangle is always 180°. So, we have:
m∠B + m∠C + m∠D = 180°
25° + 3x° + (3x + 5)° = 180°
25° + 3x° + 3x° + 5° = 180°
Combine like terms:
8x° + 30° = 180°
Subtract 30° from both sides:
8x° = 150°
Divide both sides by 8:
x° = 18.75°
So, m∠C = 3x° = 3(18.75°) = 56.25°.
To find the measure of ∠D, we can substitute the value of x into the expression for m∠D:
m∠D = 3x + 5° = 3(18.75°) + 5° = 56.25° + 5° = 61.25°.
Therefore, the measures of ∠C and ∠D are m∠C = 56.25° and m∠D = 61.25°.