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=_°

Answer 1

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°