Angles Transversal 8Dd8Da

1. **State the problem:** We have two lines cut by a transversal with given angle measures $\angle 1 = 90.5^\circ$ and $\angle 7 = 89.5^\circ$. We need to determine the truth of four statements about angle congruences and parallelism. 2. **Recall angle relationships:** - Alternate interior angles are congruent if lines are parallel. - Corresponding angles are congruent if lines are parallel. - Consecutive interior angles (same side interior) are supplementary if lines are parallel. - Vertical angles are congruent. 3. **Check $\angle 4$ and $\angle 5$:** - $\angle 4$ and $\angle 5$ are alternate interior angles. - Given $\angle 1 = 90.5^\circ$ and $\angle 7 = 89.5^\circ$, the lines are not exactly parallel (since alternate interior angles differ). - Therefore, $\angle 4$ is not congruent to $\angle 5$. 4. **Check if the two lines are parallel:** - For parallel lines, alternate interior angles must be equal. - Since $\angle 1 \neq \angle 7$, lines are not parallel. 5. **Check measure of $\angle 6$:** - $\angle 6$ is vertical to $\angle 7$, so $\angle 6 = \angle 7 = 89.5^\circ$. - Given $\angle 1 = 90.5^\circ$, $\angle 6 \neq 90.5^\circ$. 6. **Check if $\angle 2$ and $\angle 8$ are supplementary:** - $\angle 2$ and $\angle 8$ are consecutive interior angles. - For parallel lines, they sum to $180^\circ$. - Since lines are not parallel, check sum: - $\angle 2$ is vertical to $\angle 1$, so $\angle 2 = 90.5^\circ$. - $\angle 8$ is vertical to $\angle 7$, so $\angle 8 = 89.5^\circ$. - Sum: $90.5^\circ + 89.5^\circ = 180^\circ$. - So, $\angle 2$ and $\angle 8$ are supplementary. **Final answers:** - $\angle 4$ is congruent to $\angle 5$: False - The two lines are parallel: False - The measure of $\angle 6$ is $90.5^\circ$: False - $\angle 2$ and $\angle 8$ are supplementary: True