We know that the measures of angles B, C, and D together equal 180°.
Given:
- \( m \angle B = 25° \)
- \( m \angle C = 3x \)
- \( m \angle D = 3x + 5° \)
We can set up the equation:
\[ m \angle B + m \angle C + m \angle D = 180° \]
Substituting the values we have:
\[ 25° + 3x + (3x + 5°) = 180° \]
Simplifying this, we combine like terms:
\[ 25° + 3x + 3x + 5° = 180° \] \[ 25° + 5° + 6x = 180° \] \[ 30° + 6x = 180° \]
Next, we isolate the term with \( x \):
\[ 6x = 180° - 30° \] \[ 6x = 150° \]
Now, we can solve for \( x \):
\[ x = \frac{150°}{6} = 25° \]
Now that we have the value of \( x \), we can find the measures of angles C and D:
\[ m \angle C = 3x = 3(25°) = 75° \] \[ m \angle D = 3x + 5 = 3(25°) + 5° = 75° + 5° = 80° \]
Thus, the measures of the angles are:
\[ m \angle C = 75° \] \[ m \angle D = 80° \]
In conclusion:
- \( m \angle C = 75° \)
- \( m \angle D = 80° \)