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Question
Referring the adjacent figure of a parallelogram, write the answer of questions given below.
(1) If l(WZ) = 4.5 cm then l(XY) = ?
(2) If l(YZ) = 8.2 cm then l(XW) = ?
(3) If l(OX) = 2.5 cm then l(OZ) = ?
(4) If l(WO) = 3.3 cm then l(WY) = ?
(5) If m∠WZY = 120° then m∠WXY = ? and m∠XWZ = ?
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Solution
WXYZ is a parallelogram.
(1) l(XY) = l(WZ) = 4.5 cm ...(Opposite sides of a parallelogram are congruent)
(2) l(XW) = l(YZ) = 8.2 cm ...(Opposite sides of a parallelogram are congruent)
(3) l(OZ) = l(OX) = 2.5 cm ...(Diagonals of parallelogram bisect each other)
(4) l(WY) = 2 × l(WO) = 2 × 3.3 = 6.6 cm ...(Diagonals of parallelogram bisect each other)
(5) m∠WXY = m∠WZY = 120º ...(Opposite angles of a parallelogram are congruent)
Now,
m∠WZY + m∠XWZ = 180º ...(Adjacent angles of a parallelogram are supplementary)
⇒ 120º + m∠XWZ = 180º
⇒ m∠XWZ = 180º − 120º = 60º
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