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?
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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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