Referring the Adjacent Figure of a Parallelogram, Write the Answer of Questions Given Below. - Mathematics

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 = ?

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