Question

In the given figure, AB || PQ. Find the values of x and y.

Answer 1

Given, AB∥PQ.
Let CD be the transversal cutting AB and PQ at E and F, respectively.
Then,
Since CD is a straight line

∠CEB + ∠BEG + ∠GEF = 180°

⇒ 75° + 20° + ∠GEF = 180°

⇒ ∠GEF = 85°

We know that the sum of angles of a triangle is 180°.

∴ ∠GEF + ∠EGF + ∠EFG = 180

⇒ 85°+ x + 25° = 180°

⇒ 110° + x = 180°

⇒ x = 70°

And

∠FEG + ∠BEG = ∠DFQ [Corresponding Angles]

⇒ 85° + 20° = ∠DFQ

⇒ ∠DFQ = 105°

∠EFG + ∠GFQ + ∠DFQ = 180° [Since CD is a straight line]

⇒ 25° + y+ 105° = 180°

⇒ y = 50°

∴ x = 70° and y = 50°