1. **Problem 4:** Find the measure of each angle in the first diagram where lines AC and BD intersect at point E, and angle $ \angle AEC = 146^\circ $. 2. **Key fact:** When two lines intersect, opposite (vertical) angles are equal, and adjacent angles are supplementary (sum to 180°). 3. **Calculate each angle:** - a) $ \angle AEC = 146^\circ $ (given) - b) $ \angle DEB $ is vertical to $ \angle AEC $, so $ \angle DEB = 146^\circ $ - c) $ \angle CEB $ is adjacent to $ \angle AEC $, so they are supplementary: $$\angle CEB = 180^\circ - 146^\circ = 34^\circ$$ - d) $ \angle CED $ is vertical to $ \angle CEB $, so $ \angle CED = 34^\circ $$ 4. **Final answers for Problem 4:** - a) \(146^\circ$ - b) $146^\circ$ - c) $34^\circ$ - d) $34^\circ$ --- 5. **Problem 5:** Name the angles in the second diagram with point W where several lines intersect, including a right angle at $ \angle VW S $. - a) The angle opposite $ \angle PWQ $ is the vertical angle to $ \angle PWQ $. - b) The complement of $ \angle VWT $ is the angle that sums with $ \angle VWT $ to 90°. - c) Two angles supplementary to $ \angle QWR $ are the two angles adjacent to it that sum to 180° with it. - d) The supplement of $ \angle SWR $ is the angle that sums with $ \angle SWR $ to 180°. Since no numeric measures are given for these angles, the answers are naming based on angle relationships: - a) Opposite angle to $ \angle PWQ $ is $ \angle RWS $ - b) Complement of $ \angle VWT $ is $ \angle TWS $ (since $ \angle VW S $ is right angle, $ \angle VWT + \angle TWS = 90^\circ $) - c) Two angles supplementary to $ \angle QWR $ are $ \angle RWS $ and $ \angle SWP $ - d) Supplement of $ \angle SWR $ is $ \angle RWP $ --- **Summary:** - Problem 4 angles: a) 146°, b) 146°, c) 34°, d) 34° - Problem 5 angle names as above.