[tex]\angle 1 $ and $ \angle 14: alternate $ exterior $ angles; $ transversal: $ p\\\angle 4 $ and $ \angle 10: consecutive $ interior $ angles; $ transversal: $ r\\\angle 13 $ and $ \angle 15: corresponding $ angles; $ transversal: $ s\\\angle 7 $ and $ \angle 12: alternate $ interior $ angles; $ transversal: $ q\\[/tex]
Note:
A transversal cuts across two parallel lines to form different angles
- [tex]\angle 1 $ and $ \angle 14[/tex]
The transversal line that connects [tex]\angle 1 $ and $ \angle 4[/tex] is transversal p which cuts across lines r and s.
[tex]\angle 1[/tex] and [tex]\angle 14[/tex] are outside the two parallel lines, so, they are exterior angles which are located on opposite sides of transversal p.
Therefore:
[tex]\angle 1 $ and $ \angle 14[/tex] are classified as alternate exterior angles
transversal p connects both angles.
- [tex]\angle 4 $ and $ \angle 10[/tex]
[tex]\angle 4 $ and $ \angle 10[/tex] are connected by transversal r.
[tex]\angle 4 $ and $ \angle 10[/tex] are located on one side of the transversal inside the two parallel lines intercepted by the transversal. They are interior angles.
Therefore:
[tex]\angle 4 $ and $ \angle 10[/tex] are classified as consecutive interior angles.
They are connected by transversal r.
- [tex]\angle 13 $ and $ \angle 15[/tex]
[tex]\angle 13 $ and $ \angle 15[/tex] are connected by transversal s. They lie on the same side of the transversal and are therefore corresponding to each other.
Therefore:
[tex]\angle 13 $ and $ \angle 15[/tex] are classified as corresponding angles.
Transversal s connects both angles.
- [tex]\angle 7 $ and $ \angle 12[/tex]
[tex]\angle 7 $ and $ \angle 12[/tex] lie on opposite sides of transversal q that connects them. They are alternate angles that lie inside the two parallel lines.
Therefore:
[tex]\angle 7 $ and $ \angle 12[/tex] are alternate interior angles.
Transversal q connects them.
Thus:
[tex]\angle 1 $ and $ \angle 14: alternate $ exterior $ angles; $ transversal: $ p\\\angle 4 $ and $ \angle 10: consecutive $ interior $ angles; $ transversal: $ r\\\angle 13 $ and $ \angle 15: corresponding $ angles; $ transversal: $ s\\\angle 7 $ and $ \angle 12: alternate $ interior $ angles; $ transversal: $ q\\[/tex]
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