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=_°
Since the sum of the measures of angles ∠B, ∠C, and ∠D equals 180°, we can set up the equation:
25° + (3x)° + (3x + 5)° = 180°
Simplifying the equation:
25° + 3x° + 3x° + 5° = 180°
Combining like terms:
6x° + 30° = 180°
Subtracting 30° from both sides:
6x° = 150°
Dividing both sides by 6:
x° = 25°
Now we can find the measures of ∠C and ∠D:
m∠C = 3x° = 3(25°) = 75°
m∠D = 3x + 5° = 3(25°) + 5° = 75° + 5° = 80°
Therefore, the measures of ∠C and ∠D are:
m∠C = 75°
m∠D = 80°