Subject Experts Solutions for Chapter: Understanding Quadrilaterals, Exercise 1: TEST YOUR SKILLS

All squares are trapezium.

In the given figure if $\mathrm{OB}=(2x+4)$ and $\mathrm{OC}=3x+1$, find $x$.

$\mathrm{RICE}$ is a rhombus in the given figure, find $x, y$ and $z$. Justify your answer.

In the given figure $\angle \mathrm{A}=5x-8$ and $\angle \mathrm{B}=3x+4$, find all the angles of the trapezium $\mathrm{ABCD}$ in which $\mathrm{AB}\Vert \mathrm{DC}$ and $\mathrm{AD}=\mathrm{BC}$.

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The adjacent sides of a parallelogram are in the ratio $3:8$ and its perimeter is $220 \mathrm{cm}$. Find the sides of the parallelogram.

Prove that the diagonals of a rhombus bisect each other at $90°$.

$\mathrm{ABCD}$ is a rhombus if $\angle \mathrm{ADB}=50°$. Find other angles of the rhombus.

Prove that if the diagonal of a parallelogram bisects a pair of opposite angles then it is a rhombus.