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?
We know that the sum of the measures of ∠B, ∠C, and ∠D is 180°.
Therefore, we can write the equation:
m∠B + m∠C + m∠D = 180°
25° + 3x° + (3x + 5)° = 180°
Combine like terms:
25° + 6x° + 5° = 180°
Subtract 30° from both sides:
6x° = 145°
Divide both sides by 6:
x° = 24.17°
To find the measures of ∠C and ∠D, we substitute the value of x° back into the expressions:
m∠C = 3x° = 3(24.17°) = 72.5°
m∠D = 3x° + 5° = 3(24.17°) + 5° = 72.5° + 5° = 77.5°
Therefore, the measures of ∠C and ∠D are 72.5° and 77.5° respectively.