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)
Given that the sum of the measures of ∠B, ∠C, and ∠D is 180°, we can write the equation:
25° + 3x° + (3x+5)° = 180°.
Simplifying the equation, we get:
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°) = 80°.