bee171
12.10.2020 •
Mathematics
Which angle measures are correct? Select three
options.
OmZ2 = 125°
Omz3 = 55°
OmZ8= 55°
m212 = 100°
OmZ14 = 100°
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Ответ:
m∠2 = 125° is correct
m∠8 = 55° is correct
m∠14 = 100° is correct
Step-by-step explanation:
Let us solve the question using the angle formed with parallel lines
∵ Lines e and f are parallel
∴ m∠1 = m∠5 ⇒ corresponding angles
∵ m∠5 = 55°
∴ m∠1 = 55°
∵ ∠1 and ∠2 are linear pair angles
∴ m∠1 + m∠2 = 180°
→ Substitute ∠1 by 55°
∴ 55 + m∠2 = 180
→ Subtract 55 from both sides
∴ m∠2 = 125°
∴ m∠2 = 125° is correct
∵ ∠2 and ∠3 are vertically opposite angles
∴ m∠2 = m∠3
∵ m∠2 = 125°
∴ m∠3 = 125°
∴ m∠3 = 55° is incorrect
∵ ∠5 and ∠8 are vertically opposite angles
∴ m∠5 = m∠8
∵ m∠5 = 55°
∴ m∠8 = 55°
∴ m∠8 = 55° is correct
∵ ∠9 and ∠12 are vertically opposite angles
∴ m∠9 = m∠12
∵ m∠9 = 80°
∴ m∠12 = 80°
∴ m∠12 = 100° is incorrect
∵ ∠12 and ∠14 are interior supplementary angles
∴ m∠12 + m∠14 = 180°
→ Substitute ∠12 by 80°
∴ 80 + m∠14 = 180
→ Subtract 80 from both sides
∴ m∠14 = 100°
∴ m∠14 = 100° is correct
Ответ: