Answer:
From the graph attached, we know that [tex]\angle 1 \cong \angle 5[/tex] by the corresponding angle theorem, this theorem is about all angles that derive form the intersection of one transversal line with a pair of parallels. Specifically, corresponding angles are those which are placed at the same side of the transversal, one interior to parallels, one exterior to parallels, like [tex]\angle 1[/tex] and [tex]\angle 5[/tex].
We also know that, by definition of linear pair postulate, [tex]\angle 3[/tex] and [tex]\angle 1[/tex] are linear pair. Linear pair postulate is a math concept that defines two angles that are adjacent and for a straight angle, which is equal to 180°.
They are supplementary by the definition of supplementary angles. This definition states that angles which sum 180° are supplementary, and we found that [tex]\angle 3[/tex] and [tex]\angle 1[/tex] together are 180°, because they are on a straight angle. That is, [tex]m \angle 3 + m \angle 1 = 180\°[/tex]
If we substitute [tex]\angle 5[/tex] for [tex]\angle 1[/tex], we have [tex]m \angle 3 + m \angle 5 = 180\°[/tex], which means that [tex]\angle 3[/tex] and [tex]\angle 5[/tex] are also supplementary by definition.
Answer:
corresponding angles theorem
linear pair postulate
definition of supplementary angles
Step-by-step explanation:
