Question

Two parallel lines are intersected by a third line so that angles 1 and 5 are congruent. 2 parallel horizontal lines are intersected by a third line. On the first horizontal line where the third line intersects, 4 angles are created. Labeled clockwise, from uppercase left, the angles are 1, 2, 4, 3. On the second horizontal line, where the third line intersects, 4 angles are created. Labeled clockwise, from uppercase left, the angles are 5, 6, blank, blank. Which statement is true about angles 3 and 5? They are acute. They are congruent. They are complementary. They are supplementary.

Answer 1

"They are supplementary" ⇒ last answer

Explanation:

* Look to the attached figure

- Two parallel horizontal lines are intersected by a third line

- The angles formed form intersection are labeled on the figure

- From the two parallel lines and

∠5 ≅ ∠1 ⇒ corresponding angles

m∠5 = m∠1

- A linear pair is two angles that are adjacent and form a line and

they are supplementary

∠1 and ∠3 form a line

∠1 and ∠3 are linear pair

* lets prove that ∠3 and ∠5 are supplementary

∵ m∠1 = m∠5 ⇒ corresponding angles

∵ ∠1 and ∠3 form a linear pair

∵ Linear pair are supplementary

∴ m∠1 + m∠3 = 180°

- By substitute ∠1 by ∠5

∴ m∠5 + m∠3 = 180

∴ ∠5 and ∠3 are supplementary

* The true statement is "They are supplementary"