Two parallel lines are intersected by a third line so that angles 1 and 5 are congruent. 2 parallel horizontal lines are interse
cted 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.
2 answers:
Answer:
"They are supplementary" ⇒ last answer
Step-by-step explanation:
* <em>Look to the attached figure</em>
- 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
* <em>lets prove that ∠3 and ∠5 are supplementary</em>
∵ 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"
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