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Ray Of Light [21]
3 years ago
12

two parallel lines are cut by a transversal as shown below. Suppose m<8=131. Find m<1 and m<3.

Mathematics
1 answer:
Olegator [25]3 years ago
4 0

Answer:

m∠1 is 49° and m∠3 is 49°

Step-by-step explanation:

In the given figure

∵ There are 2 parallel lines

∵ A transversal cuts them

∴ ∠4 and ∠8 are corresponding angles

→ Corresponding angles are equal in measures

∴ m∠4 = m∠8

∵ m∠8 = 131°

∴ m∠4 = 131°

∵ ∠1 and ∠4 formed a pair of linear angle

∵ The sum of the measures of the linear angles is 180°

∴ m∠1 + m∠4 = 180°

→ Substitute ∠4 by 131°

∴ m∠1 + 131° = 180°

→ Subtract 131 from both sides

∵ m∠1 + 131 - 131 = 180 - 131

∴ m∠1 = 49°

∵ ∠1 and ∠3 are vertically opposite angles

∴ m∠1 = m∠3

∵ m∠1 = 49°

∴ m∠3 = 49°

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