Maharashtra Board Solutions for Chapter: Quadrilaterals, Exercise 1: Practice set 5.1

Diagonals of a parallelogram $\mathrm{WXYZ}$ intersect each other at point $\mathrm{O}$. If $\angle \mathrm{XYZ} = 135°$then what is the measure of $\angle \mathrm{XWZ}$ and $\angle \mathrm{YZW}?$ If$\mathrm{l}\left(\mathrm{OY}\right)= 5 \mathrm{cm}$ then $\mathrm{l}\left(\mathrm{WY}\right)=?$ [write the final answer in numericals without units]

In a parallelogram $\mathrm{ABCD}$, if $\angle \mathrm{A}=(3x+12)°$, $\angle \mathrm{B}=(2x-32)°$, then find the value of $x$ and then find the measures of $\angle \mathrm{C}$ and $\angle \mathrm{D}$.

Perimeter of a parallelogram is $150 \mathrm{cm}$. One of its sides is greater than the other side by $25 \mathrm{cm}$. Find the lengths of all sides.

If the ratio of measures of two adjacent angles of a parallelogram is $1:2$, find the measures of all angles of the parallelogram.

Diagonals of a parallelogram intersect each other at point $\mathrm{O}$. If $AO= 5$, $BO=12$ and $AB=13$ then, show that quadrilateral $ABCD$ is a rhombus.

In the figure, $\mathrm{PQRS}$ and $\mathrm{ABCR}$ are two parallelograms. If $\angle \mathrm{P} = 110°$ then, find the measures of all angles of $\mathrm{ABCR}$.

In figure, $\mathrm{ABCD}$ is a parallelogram. Point$\mathrm{E}$ is on the ray $\mathrm{AB}$ such that $\mathrm{BE}=\mathrm{AB}$, then prove that line $\mathrm{ED}$ bisects segment $\mathrm{BC}$ at point $\mathrm{F}$.