1a. Identify the pairs of vertically opposite angles. b. Identify the corresponding angles. c. Identify the alternate angles. d. Identify all angles that will be equal to the one marked.

Here are the identified angle pairs and equal angles for each diagram. 1a. Identify the pairs of vertically opposite angles. Vertically opposite angles are formed when two lines intersect; they are opposite each other and are always equal. i. (top-left angle at top intersection, bottom-right angle at top intersection) (top-right angle at top intersection, bottom-left angle at top intersection) (top-left angle at bottom intersection, bottom-right angle at bottom intersection) (top-right angle at bottom intersection, bottom-left angle at bottom intersection) ii. (top-left angle at left intersection, bottom-right angle at left intersection) (top-right angle at left intersection, bottom-left angle at left intersection) (top-left angle at right intersection, bottom-right angle at right intersection) (top-right angle at right intersection, bottom-left angle at right intersection) 1b. Identify the corresponding angles. Corresponding angles are in the same relative position at each intersection. These angles are equal if the lines are parallel (which is assumed for these diagrams). i. (Assuming the two horizontal lines are parallel) (top-left angle at top intersection, top-left angle at bottom intersection) (top-right angle at top intersection, top-right angle at bottom intersection) (bottom-left angle at top intersection, bottom-left angle at bottom intersection) (bottom-right angle at top intersection, bottom-right angle at bottom intersection) ii. (Assuming the two vertical lines are parallel) (top-left angle at left intersection, top-left angle at right intersection) (top-right angle at left intersection, top-right angle at right intersection) (bottom-left angle at left intersection, bottom-left angle at right intersection) (bottom-right angle at left intersection, bottom-right angle at right intersection) 1c. Identify the alternate angles. Alternate angles are on opposite sides of the transversal. Alternate interior angles are between the parallel lines, and alternate exterior angles are outside the parallel lines. These angles are equal if the lines are parallel (which is assumed for these diagrams). i. (Assuming the two horizontal lines are parallel) Alternate interior: (bottom-left angle at top intersection, top-right angle at bottom intersection) and (bottom-right angle at top intersection, top-left angle at bottom intersection). Alternate exterior: (top-left angle at top intersection, bottom-right angle at bottom intersection) and (top-right angle at top intersection, bottom-left angle at bottom intersection). ii. (Assuming the two vertical lines are parallel) Alternate interior: (top-right angle at left intersection, bottom-left angle at right intersection) and (bottom-right angle at left intersection, top-left angle at right intersection). Alternate exterior: (top-left angle at left intersection, bottom-right angle at right intersection) and (bottom-left angle at left intersection, top-right angle at right intersection). 1d. Identify all angles that will be equal to the one marked. For parallel lines, all acute angles are equal to each other, and all obtuse angles are equal to each other. i. The marked angle is the top-right angle at the bottom intersection*. This is an obtuse angle. The angles equal to it are: The marked angle itself (top-right angle at bottom intersection) The bottom-left angle at the bottom intersection (vertically opposite) The top-right angle at the top intersection (corresponding) The bottom-left angle at the top intersection (vertically opposite to the corresponding angle) ii. The marked angle is the top-left angle at the left intersection*. This is an acute angle. The angles equal to it are: The marked angle itself (top-left angle at left intersection) The bottom-right angle at the left intersection (vertically opposite) The top-left angle at the right intersection (corresponding) The bottom-right angle at the right intersection (vertically opposite to the corresponding angle) Drop the next question! 📐