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ago in Plane Geometry and Line and Angle by (28.2k points)
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In the given figure, AB || EF. Find ∠x and ∠y

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Best answer

∵ AB || EF (given)

Also draw a line through P parallel to AB or EF

∴ 125°+ ∠APQ = 180°

(sum of the interior angles on the same side of a transversal is 180°)

⇒ ∠APQ = 180°- 125°

⇒ ∠APQ = 55°

Also PQ || EF (by const.)

∠QPE + 141°= 180°

(reason as above )

⇒ ∠QPE = 39°

∴ ∠x = 55° + 39° = 94°

and ∠y = 360° – 94° = 266°

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