S Purkayastha Solutions for Chapter: The Triangle and its Properties, Exercise 2: Check Point

The base angle of an isosceles triangle is $24°$ more than the vertical angle. Find the measure of each angle.

The vertical angle of a triangle is $63°$ and the base angles are in the ratio of $5:4$. Find the measure of each base angle.

In figure, $△ABC$ is right angled at $C$, and $CD\perp AB$. Also $\angle A=65°$.  Find $k$, if $\angle ACD$ is $k°$.

In figure, $△ABC$ is right angled at $C$, and $CD\perp AB$. Also $\angle A=65°$.  Find $k$, if $\angle BCD$ is $k°$.

In figure, $△ABC$ is right angled at $C$, and $CD\perp AB$. Also $\angle A=65°$.  Find $k$, if $\angle CBD$ is $k°$.

In $△ABC, \angle A=100°, AD$ bisects $\angle A$ and $AD\perp BC$. Find $k$, if $\angle B$ is $k°$.

In figure, $△ABC, \angle A=70°, \angle B=60°$ and the bisectors of $\angle B$ and $\angle C$ meet at $O$.  Find $k$, if $\angle C$ is $k°$. 

In figure, $△ABC, \angle A=70°, \angle B=60°$ and the bisectors of $\angle B$ and $\angle C$ meet at $O$.  Find $k$, if $\angle BOC$ is $k°$.