22.	+Angles+formed+when+two+non+parallel+lines+are+cut+by+a+transversal

Angles formed when two non parallel lines are cut by a transversal by, Drew Katz and David Levine On this wiki page our group will help teach you about when angles are formed when two non parallel lines are cut by a transversal. This wiki page will provide a brief summary about our topic, multiple example problems using extensive knowledge on the topic, and four other helpful websites linked to this page. When angles are formed by two non parallel lines that are cut by a third line known as the transversal multiple pairs of angles are formed. One example of the angles are known as vertical pairs. Each vertical pair consists of two congruent vertical angles, look to diagram 1 for visual understanding. Another thing that is created by this are known as supplementary pairs, which will add up to 180 degrees. There will be eight supplementary pairs made, look to the first diagram to further understand it with visualizations. Alternate interior angles which are two angles on the inside of the two lines that are along the transversal and opposite to each other. There will be two pairs of these, find diagram 2 to see alternate interior angles Alternate exterior angles are created also. These are two angles that are on the outside of the two lines and opposite each other along the transversal, like alternate interior angles two angle pairs will be formed and find diagram 3 to see alternate exterior angles. Corresponding angles are another example of angles formed. They are two angles one on the outside of the lines and one on the inside that are both on the right or left side of the transversal and see diagram 4 for a visual. Two other types of angles created are consecutive interior angles which are angles in the interior that are on the same side of the transversal and consecutive exterior angles which are angles on the outside of the two parallel lines that are on the same side and refer to diagram 5 for a visual. Here are examples of each: Diagram 1: Questions referring to diagram 1: 1. Q :The measure of angle 2 is 30 degrees, then what would the measure of angle 3 be? A: **The measure of angle 3 would be 30 degrees as well because they are vertical angles and all vertical angles are congruent. 2. Q: If the measure of angle of 2 is 30 degrees, what would the measure of ** angle 4 be? A: **The measure of angle 4 would be 150 degrees because angle's 2 and 4 are supplementary which means they add up to 180. 3. Q: Given that the measure of angle 1 is 52 degrees and angle 5 is 50 degrees find the measure of angles 2 through 8 and state reasons why? A: Angle 2= 128 degrees because angle 1 and angle 2 are supplements, Angle 3= 128 degrees because angle 3 is a vertical angle to angle 2 which equals 128, Angle 4= 52 degrees because angle 4 is a vertical angle to angle 1,, Angle 6= 130 degrees because it and angle 5 are supplementary, Angle 7= 130 degrees because Angle 6 is congruent to it by vertical angles, and Angle 8= 50 because Angle 5 is congruent to it by vertical angles. 4. Q: Name the alternate interior and exterior angles? ****A: Alternate Interior: <3 and <6, <4 and <5. Alternate Exterior: <1 and <8, <2 and <7.**



Supplementary Angles: <1 and <2 <2 and <4 <3 and <4 <1 and <3 <5 and <6 <6 and <8 <7 and <8 <5 and <7 Vertical Angles (congruent): <1 and <4 <2 and <3 <5 and <8 <6 and <7 Diagram 2:

Alternate interior angles: Figure 1- <4 and <5 Figure 2- <3 and <6 Diagram 3: Alternate Exterior Angles: Figure 1- <1 and <8 Figure 2- <2 and <7 Diagram 4: Corresponding Angles : Figure 1- <1 and <5 Figure 2- <2 and <6 Figure 3- <3 and <7 Figure 4- <4 and <8 Diagram 5:

Consecutive Interior Angles: <4 and <5 <3 and <6 Consecutive Exterior Angles: <1 and <8 <2 and <7

Here are some additional websites to help you understand the topic: [|Forming angles when moving the transversal*] [|More additional understanding] [|More understanding all the angles formed]