3. If \( \angle A \) and \( \angle B \) are supplementary angles and \( \angle A \) is three times as large as \( \angle B \), find the measures of \( \angle A \) and \( \angle B \).

To solve for the measures of \( \angle A \) and \( \angle B \), we start with the given information. Since \( \angle A \) and \( \angle B \) are supplementary, we know that: \[ \angle A + \angle B = 180^\circ \] Furthermore, we know that: \[ \angle A = 3 \angle B \] Now, we can substitute \( \angle A \) in the first equation with \( 3 \angle B \): \[ 3 \angle B + \angle B = 180^\circ \] This simplifies to: \[ 4 \angle B = 180^\circ \] Now, divide both sides by 4: \[ \angle B = \frac{180^\circ}{4} = 45^\circ \] Now, we can find \( \angle A \): \[ \angle A = 3 \angle B = 3 \times 45^\circ = 135^\circ \] Thus, the measures of the angles are: \(\angle A = 135^\circ\) and \(\angle B = 45^\circ\).