Question

A transversal intersects two parallel lines. The measures of a pair of alternate interior angles are 5v and​ 2w. The measures of a pair of​ same-side exterior angles are 10w and 5v. What are the values of w and​ v?

Answer 1

Step-by-step explanation:

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Answer 2

Given :- (from image)

• Transversal l intersecting two parallel lines m and n .
• ∠GBE = 5v and ∠BED = 2w are a pair of alternate interior angles .
• ∠ABC = 10w and ∠DEF = 5v are a pair of same-side exterior angles .

To Find :-

• What are the values of w and v ?

Solution :-

we know that,

• when the two lines being crossed are parallel lines the Alternate Interior Angles are equal.
• Exterior angles on the same side of the transversal are supplementary (sum equal to 180°).

So,

→ ∠GBE = ∠BED (Alternate Interior Angles are equal.)

→ 5v = 2w --------- Eqn.(1)

and,

→ ∠ABC + ∠DEF = 180° (Exterior angles on the same side of the transversal are supplementary .)

→ 5v + 10w = 180°

putting value of 5v from Eqn.(1) ,

→ 2w + 10w = 180°

→ 12w = 180°

→ w = 15° (Ans.)

Putting value of w in Eqn.(1) ,

→ 5v = 2 * 15

→ 5v = 30

→ v = 6° (Ans.)

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