From the graph attached, we know that $\angle 1 \cong \angle 5$ 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 $\angle 1$ and $\angle 5$ .

We also know that, by definition of linear pair postulate, $\angle 3$ and $\angle 1$ 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 $\angle 3$ and $\angle 1$ together are 180°, because they are on a straight angle. That is, $m \angle 3 + m \angle 1 = 180\°$

If we substitute $\angle 5$ for $\angle 1$ , we have $m \angle 3 + m \angle 5 = 180\°$ , which means that $\angle 3$ and $\angle 5$ are also supplementary by definition.

4 0

3 years ago

Read 2 more answers