O P Malhotra, S K Gupta and, Anubhuti Gangal Solutions for Exercise 1: Exercise

Calculate the angles marked with small letters in the diagram drawn below.

Find each angle of a parallelogram if two consecutive angles are in the ratio of $1: 5$.

Find the size of the angles of a parallelogram if one angle is $20°$ less than twice the smallest angle.

If an angle of rhombus is $50°$, find the size of the angles of one of the triangles which are formed by the diagonals.

If an angle of a parallelogram is two-thirds its adjacent angle, find the angles of the parallelogram.

$ABCD$ is a parallelogram in which $\angle DAB=70°,\angle DBC=80°,$ calculate angles $CDB$ and $ADB.$

$PQRS$ is a rhombus in which the diagonal $\mathrm{PR}$ is produced to $\mathrm{T}.$ If $\angle SRT=152°$$,$ then find $\mathrm{x}, \mathrm{y},$ and $\mathrm{z}.$ 

$ABCD$ is a rhombus and $ABE$ is an equilateral triangle. $\angle BCD=78°.$ Calculate $\angle ADE, \angle BDE$ and $\angle BED.$