Q1 of 35 Page 62

Diagonals of a parallelogram 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)=?


Given ZX and WY are the diagonals of the parallelogram


∠ XYZ = 135° ⇒ ∠ XWZ = 135° as the opposite angels of a parallelogram are congruent.


∠YZW + ∠ XWZ = 180° as the adjacent angels of the parallelogram are supplementary.


⇒ ∠YZW = 180° - 135° = 45°


Length of OY = 5 cm then length of WY = WO + OY = 5+5 = 10 cm


(diagonals of the parallelogram bisect each other. So, O is midpoint of WY)


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