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=
We know that the sum of the measures of all three angles is 180°. Therefore, we can write the equation:
25° + (3x)° + (3x+5)° = 180°
Simplifying this equation, we have:
25° + 6x° + 5° = 180°
Combining the like terms:
30° + 6x° = 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 using the value of x we found:
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° and m∠D = 80°.