Question

Please help, the question is why which angle is congruent to <1 and the answers are

14
7
4
13

Answer 1

Answer: angle 14

Reason: Alternate exterior angle theorem

If you want, erase line m and the associated angles with it, to avoid unnecessary clutter.

The key thing to focus on is that line s is parallel to line t, so alternate exterior angles 1 and 14 are congruent. They are exterior because they are outside the parallel lines. They are considered "alternating" since they are on opposite sides of the transversal line L.

Here are some alternate proofs to show that angles 1 and 14 are congruent.

• Show that angle1 = angle 9 (corresponding angles), then use the idea that angle9=angle14 (vertical angles). Lastly, tie them together with the transitive property to arrive at angle1=angle14.
• angle1 = angle6 (vertical angles). Then angle6 = angle9 (alternate interior angles) and angle9=angle14 (vertical angles). Use the transitive property twice to arrive at angle1=angle14.

Other proofs are possible.