Angle Sum Property of a Triangle

Sides $BC, CA \mathrm{and} BA$ of a triangle $ABC$ are produced to $D, Q \mathrm{and} P$ respectively, as shown in figure. If $\angle ACD=100° \mathrm{and} \angle QAP=35°$, find all the angles of the triangle.

In figure, find the values of unknown quantities.

In figure, find the values of unknown quantities.

In figure, find the value of $k$ if $x=k°$.

In figure, find the value of $k$ if $x=k°$.

In figure, $DA=DB=DC, DB$ bisects $\angle ABC$ and $\angle ADB=60°$. Find the value of $k$ if $x=k°$.

In figure, $△EAB$ is an equilateral triangle and $ABCD$ is a square. Find the values of $x \mathrm{and} y$.

An exterior angle of a triangle is of the measure $70°$ and one of its interior opposite angles is of the measure $25°$. Find the measure of the other interior angles.

The angles of a triangle are in the ratio $1:2:3$. Find the angles.

In a $△ABC, \angle A=\angle B$ and $\angle C=50°$. Find $\angle A$ and $\angle B$,

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 $k°$. 

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

A tree is broken by the wind at $5 \mathrm{m}$ above the ground in such a way that is top touches the ground $12 \mathrm{m}$ away from the bottom of the tree. What was the height of the tree before it broke off $?$

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

In $△ABC$, if $2\angle A=3\angle B=6\angle C,$ calculate the measure of $\angle A, \angle B$ and $\angle C$.

$($ Hint: Let $2\angle A=3\angle B=6\angle C=x\Rightarrow \angle A=\frac{x}{2}, \angle B=\frac{x}{3},\angle C=\frac{x}{6}$$)$

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.

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