A K Upadhyay and S Upadhyay Solutions for Chapter: Quadrilaterals, Exercise 2: EXERCISE

Three angles of a quadrilateral measure $100°,\mathrm{}98°,\mathrm{}92°$. If the fourth angle is $k°$ then find $k$.

In Figure, $P \&\hspace{0.17em}Q$ are mid points of the sides $\mathrm{A}\mathrm{B}$ and $\mathrm{A}\mathrm{C}$ respectively of $∆\mathrm{A}\mathrm{B}\mathrm{C}$. Also $\mathrm{D}$ and $\mathrm{E}$ are mid-points of $\mathrm{A}\mathrm{P}$ and $\mathrm{A}\mathrm{Q}$ respectivley. If $\mathrm{D}\mathrm{E}=2.3\mathrm{}\mathrm{c}\mathrm{m}$ and $\mathrm{B}\mathrm{C}=\mathrm{k} \mathrm{cm}$ then find $k$.

In Figure, $\mathrm{P}\mathrm{Q}\mathrm{R}\mathrm{S}$ is a square. A line $\mathrm{S}\mathrm{M}$ cuts the side $\mathrm{Q}\mathrm{R}$ at $\mathrm{M}$ and the diagonal $\mathrm{P}\mathrm{R}$ at $\mathrm{O}$ such that $\mathrm{\angle }\mathrm{R}\mathrm{O}\mathrm{S}=110°$ and $\mathrm{\angle }\mathrm{S}\mathrm{M}\mathrm{R}=x°$. Find the value of $x$.

In Figure, $\mathrm{A}\mathrm{B}\mathrm{C}\mathrm{D}$ is a parallelogram $\mathrm{E}$ is the midpoint. $\mathrm{D}\mathrm{F}$ is drawn parallel to $\mathrm{E}\mathrm{B}$ to meet $\mathrm{C}\mathrm{B}$ produced at $\mathrm{G}$ and it cuts $\mathrm{A}\mathrm{B}$ at $\mathrm{F}$. Prove that
$\mathrm{A}\mathrm{D}=1/2\mathrm{G}\mathrm{C}$

In Figure, $\mathrm{A}\mathrm{B}\mathrm{C}\mathrm{D}$ is a parallelogram $\mathrm{E}$ is the midpoint. $\mathrm{D}\mathrm{F}$ is drawn parallel to $\mathrm{E}\mathrm{B}$ to meet $\mathrm{C}\mathrm{B}$ produced at $\mathrm{G}$ and it cuts $\mathrm{A}\mathrm{B}$ at $\mathrm{F}$. Prove that
$\mathrm{D}\mathrm{G}=2\mathrm{E}\mathrm{B}$

In Figure, $\mathrm{A}\mathrm{B}\mathrm{C}\mathrm{D}$ and $\mathrm{P}\mathrm{Q}\mathrm{R}\mathrm{C}$ arc rectangles and $\mathrm{Q}$ is the midpoint of $\mathrm{A}\mathrm{C}$. Prove that
$\mathrm{D}\mathrm{P}=\mathrm{P}\mathrm{C}$

In Figure, $\mathrm{A}\mathrm{B}\mathrm{C}\mathrm{D}$ and $\mathrm{P}\mathrm{Q}\mathrm{R}\mathrm{C}$ arc rectangles and $\mathrm{Q}$ is the midpoint of $\mathrm{A}\mathrm{C}$. Prove that
$\mathrm{P}\mathrm{R}=1/2\mathrm{A}\mathrm{C}$

Prove that the opposite angles of an isosceles trapezium are supplementary.