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Diagonals of a parallelogram WXYZ intersect each other at point O. If ∠XYZ ∠ = 135°, then measure of ∠XWZ and ∠YZW? If l(OY) = 5 cm, then l(WY) = ?

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i. ∠XYZ = 135° 

□ WXYZ is a parallelogram.

∠XWZ = ∠XYZ 

∴ ∠XWZ = 135° …..(i) 

ii. ∠YZW + ∠XYZ = 180° [Adjacent angles of a parallelogram are supplementary] 

∴ ∠YZW + 135°= 180° [From (i)] 

∴ ∠YZW = 180°- 135° 

∴ ∠YZW = 45°

iii. l(OY) = 5 cm [Given] 

l(OY) = (1/2) l(WY) [Diagonals of a parallelogram bisect each other] 

∴ l(WY) = 2 x l(OY) = 2 x 5 

∴ l(WY) = 10 cm 

∴ ∠XWZ = 135°, ∠YZW = 45°, l(WY) = 10 cm

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