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?
Since the sum of the measures of∠B, ∠C, and ∠D is 180°, we can set up the equation:
m∠B + m∠C + m∠D = 180°
25° + 3x + 3x + 5 = 180°
25° + 6x + 5 = 180°
30 + 6x = 180
6x = 150
x = 25
Therefore, the measure of ∠C is 3x = 3(25) = 75°, and the measure of ∠D is 3x + 5 = 3(25) + 5 = 75° + 5° = 80°.