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Condition for Two Lines to Be Parallel

In the given ...

Question

In the given figure, 𝒑||𝒒 and 𝒍 is a transversal. Find the values of 𝒙 and 𝒚.

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Solution

6x + y = x + 5y
⇒ 6x - x = 5y - y (Corresponding angles are equal)
⇒ x = 4y/5
4x + (6x + y) = 180° (linear pair of angles)
10x + y = 180°
0(4y/5) + y = 180° (Substituting x = 4y/5)
9y = 180°
y = 20°
Substitute y = 20° in x = 4y/5
x = (4(20° ))/5
⇒ x = 16°

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