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Question
Diagonals of a parallelogram `square`WXYZ intersect each other at point O. If ∠XYZ = 135° then what is the measure of ∠XWZ and ∠YZW?
If l(OY)= 5 cm then l(WY)= ?
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Solution
Figure:
i. ∠XYZ = 135°
`square`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]
I(OY) = `1/2` I(WY) ...[Diagonals of a parallelogram bisect each other]
∴ I(WY) = 2 × l(OY)
∴ I(WY) = 2 × 5
∴ I(WY) = 10 cm
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