We know that the sum of the measures of angles \( \angle B, \angle C, \) and \( \angle D \) is \( 180^\circ \). We are given the following measures:
- \( m\angle B = 25^\circ \)
- \( m\angle C = 3x \)
- \( m\angle D = 3x + 5 \)
We can set up the equation based on the sum of the angles:
\[ m\angle B + m\angle C + m\angle D = 180^\circ \]
Substituting in the values we have:
\[ 25 + 3x + (3x + 5) = 180 \]
Combining like terms:
\[ 25 + 3x + 3x + 5 = 180 \] \[ 25 + 5 + 6x = 180 \] \[ 30 + 6x = 180 \]
Now, we can solve for \( x \):
\[ 6x = 180 - 30 \] \[ 6x = 150 \] \[ x = 25 \]
Now that we have \( x \), we can find the measures of \( \angle C \) and \( \angle D \):
\[ m\angle C = 3x = 3(25) = 75^\circ \]
\[ m\angle D = 3x + 5 = 3(25) + 5 = 75 + 5 = 80^\circ \]
Thus, the measures of \( \angle C \) and \( \angle D \) are:
\[ m\angle C = 75^\circ \]
\[ m\angle D = 80^\circ \]
Final answers:
- \( m\angle C = 75^\circ \)
- \( m\angle D = 80^\circ \)
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