Question

Referring the adjacent figure of a parallelogram, write the answers 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 = ?

Answer 1

Hi ,

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We know the properties of the parallelogram

1) Opposite sides are parallel and equal.

2 ) Opposite angles are equal.

3 ) Sum of the adjecent angles are

supplementary.

4 ) Diagonals are bisects each other.

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Here ,

1 ) I( XY ) = I( WZ ) = 4.5

2 ) I( XW ) = I( YZ ) = 8.2

3 ) I( OZ ) = I( OX ) = 2.5

4 ) I( WY ) = 2 × I( WO ) = 2 × 3.3 = 6.6

5 ) m<WXY = m<WZY = 120°

6 ) m<XWZ + m<WZY = 180°

m<XWZ + 120° = 180°

m<XWZ = 180° - 120°

m<XWZ = 60°

I hope this helps you.

: )

Answer 2

Solution :-

(1) If WZ = 4.5 cm then XY = 4.5 cm (Opposite sides of a parallelogram are parallel and equal)

(2) If YZ = 8.2 cm then XW = 8.2 cm (Opposite sides of a parallelogram are parallel and equal)

(3) If OX = 2.5 cm then OZ = 2.5 cm (Diagonals of a parallelogram bisect each other)

(4) If WO = 3.3 cm then WY = (2*WO) = (2*3.3) = 6.6 cm

(5) If m∠WZY = 120° then m∠WXY = 120° (Opposite angles of a parallelogram are of equal measure)

If m∠WZY = 120° then mXWZ = 60° (Sum of the adjacent angles of a parallelogram is always 180° hence they are supplementary)

∠WZY + ∠XWZ = 180°

120° + ∠XWZ = 180°

∠XWZ = 180° - 120°

∠XWZ = 60°

Answer.