Embibe Experts Solutions for Chapter: Geometry, Exercise 4: Quadrilaterals

If the bisectors of two adjacent angles are perpendicular, the adjacent angles are the angles:

Three acute angles of a quadrilateral are $82°$ each. Find out the fourth angle. 

The ratio between the angles of a quadrilateral is $3:4:6:5$. Two-third of the largest angle of the quadrilateral is equal to the smaller angle of a parallelogram. What is the value of the adjacent angle of the parallelogram?

$\mathrm{ABCD}$ is a quadrilateral in which diagonal $\mathrm{BD}=64 \mathrm{cm}$, $\mathrm{AL}\perp \mathrm{BD}$ and $\mathrm{CM}\perp \mathrm{BD}$, such that, $\mathrm{AL}=13.2 \mathrm{cm}$ and CM$\mathrm{CM} =16.8 \mathrm{cm}$. The area of the quadrilateral $\mathrm{ABCD}$ in square centimetres is:

If angles of a quadrilateral are in the ratio $3:5:9:13$, find the largest angle.

The four angles of a quadrilateral are ${\mathrm{A}}_1, {\mathrm{A}}_2, {\mathrm{A}}_3$ and ${\mathrm{A}}_4$. The sum of ${\mathrm{A}}_1$ and ${\mathrm{A}}_2$ is greater than ${\mathrm{A}}_3$ by $20°$ and ${\mathrm{A}}_4$ is greater than ${\mathrm{A}}_3$ by $70°$. What is the sum of ${\mathrm{A}}_1$ and ${\mathrm{A}}_2$?

$\mathrm{P}$ is any point in the quadrilateral$\mathrm{ABCD}$and measure of angle $\mathrm{APB}$is $70°$. The measure of angle$\mathrm{DPC}$is: 

ABCD is a quadrilateral. If P, Q, R, S are the points of bisection of the sides AB, BC, CD and DA, respectively and are adjacent to A and C, then PQRS is a: