We know that the measures of \(\angle B\), \(\angle C\), and \(\angle D\) add up to 180 degrees:
\[ m<B + m<C + m<D = 180 \]
Given that \(m<B = 25\), \(m<C = 3x\), and \(m<D = 3x + 5\), we can substitute these values into the equation:
\[ 25 + 3x + (3x + 5) = 180 \]
Now, let's simplify the left side:
\[ 25 + 3x + 3x + 5 = 180 \] \[ 25 + 5 + 6x = 180 \] \[ 30 + 6x = 180 \]
Next, we isolate \(6x\):
\[ 6x = 180 - 30 \] \[ 6x = 150 \]
Now, solve for \(x\):
\[ x = \frac{150}{6} = 25 \]
Now that we have \(x\), we can find the measures of \(\angle C\) and \(\angle D\):
- For \(\angle C\):
\[ m<C = 3x = 3(25) = 75 \]
- For \(\angle D\):
\[ m<D = 3x + 5 = 3(25) + 5 = 75 + 5 = 80 \]
So the measures of \(\angle C\) and \(\angle D\) are:
\[ m<C = 75 \] \[ m<D = 80 \]