Question

Together, the measure 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?

Answer 1

[AI-generated answer — Bot GPT 3.5]

The sum of the measures of angles B, C, and D is 180°:

m B + m C + m D = 180
25° + (3x)° + (3x + 5)° = 180
25° + 3x° + 3x° + 5° = 180
Combine like terms:
25° + 5° = 180 - 3x° - 3x°
30° = 180 - 6x°
Subtract 180 from both sides of the equation:
30° - 180 = 180 - 180 - 6x°
-150 = -6x°
Divide both sides by -6:
-150/-6 = -6x/-6
25 = x
Now, plug in the value of x into the expressions for m C and m D:
m C = 3x° = 3(25°) = 75°
m D = 3x + 5° = 3(25°) + 5° = 75° + 5° = 80°
So, the measure of angle C is 75°, and the measure of angle D is 80°.