Angle Sum Property of a Triangle

Prove that sum of interior angles in a triangle is $180°$.

If the sides of a triangle are produced in order and the sum of exterior angles thus formed is $k°$. Find the value of $k$.

Using information given in the figure, calculate the value of $x$ and $y$.

In the adjacent figure, it is given that $\mathrm{AB}=\mathrm{AC}, \angle \mathrm{BAC}=36° \mathrm{and} \angle \mathrm{AEC}=40°$. If $\angle \mathrm{EAC}=k°$, then find the value of $k$.

In the adjacent figure, it is given that $\mathrm{AB}=\mathrm{AC}, \angle \mathrm{BAC}=36° \mathrm{and} \angle \mathrm{AEC}=40°$. If $\angle \mathrm{DAB}=k°$, then find the value of $k$.

In the adjacent figure, it is given that $\mathrm{AB}=\mathrm{AC}, \angle \mathrm{BAC}=36° \mathrm{and} \angle \mathrm{AEC}=40°$. If $\angle \mathrm{ACB}=k°$, find $k$.

In the adjacent figure, it is given that $\mathrm{AB}=\mathrm{AC}, \angle \mathrm{BAC}=36° \mathrm{and} \angle \mathrm{AEC}=40°$. If $\angle \mathrm{ABC}=k°$, find $k$.

In the given figure $△\mathrm{ABC},$ side $\mathrm{AC}$ has been produced to $\mathrm{D}. \angle \mathrm{BCD}=125° \mathrm{and} \angle \mathrm{A}:\angle \mathrm{B}=2:3$, find the measure of $\angle \mathrm{A} \mathrm{and} \angle \mathrm{B}$.

In the given figure if $\mathrm{PQ}\perp \mathrm{PS}, \mathrm{PQ}\parallel \mathrm{SR}, \angle \mathrm{SQR}=28° \mathrm{and} \angle \mathrm{QRT}=65°$, then find the values of $x$ and $y$.

In the adjacent figure, $\mathrm{ABC}$ is a triangle in which $\angle \mathrm{B}=50° \mathrm{and} \angle \mathrm{C}=70°$. Sides $\mathrm{AB} \mathrm{and} \mathrm{AC}$ are produced. If $\text{'}z\text{'}$ is the measure of the angle between the bisectors of the exterior angles so formed, then find $\text{'}z\text{'}$.

In the given figure if line segments $\mathrm{PQ} \mathrm{and} \mathrm{RS}$ intersect at point $\mathrm{T}$, such that $\angle \mathrm{PRT}=40°, \angle \mathrm{RPT}=95° \mathrm{and} \angle \mathrm{TSQ}=75°$, find $\angle \mathrm{SQT}$.

In the given figure if $\mathrm{AB}\parallel \mathrm{DE}, \angle \mathrm{BAC}=35°$ and $\angle \mathrm{CDE}=53°$, if $\angle \mathrm{DCE}=k°$, find $k$.

In the given figure $\angle \mathrm{X}=62°, \angle \mathrm{XYZ}=54°$. In $△\mathrm{XYZ}$ if $\mathrm{YO}$ and $\mathrm{ZO}$ are bisectors of $\angle \mathrm{XYZ} \mathrm{and} \angle \mathrm{XZY}$ respectively find $\angle \mathrm{OZY} \mathrm{and} \angle \mathrm{YOZ}$.

In the given figure sides $\mathrm{QP}$ and $\mathrm{RQ}$ of $△\mathrm{PQR}$ are produced to points $\mathrm{S}$ and $\mathrm{T}$ respectively. If $\angle \mathrm{SPR}=135°$ and $\angle \mathrm{PQT}=110°$, if $\angle \mathrm{PRQ}=k°$, find $k$.

Find the values of $x$ and $y$ in the given figure.

In the given figure $\mathrm{AS}\parallel \mathrm{BT}; \angle 4=\angle 5. \overline{\mathrm{SB}}$ bisects $\angle \mathrm{AST}$. If the measure of $\angle 1=k°$, find $k$.

In the given triangle, if $y=k°$, find $k$.

In the given triangle, if $z=k°$, find $k$.

In the given triangle, if $x=k°$, find $k$.

$ABC$ is a triangle in which $BC$ is produced to $D$, $CA$ is produced to $E$, $\angle DCA = 108°$ and$\angle EAB = 124°.$ If $\angle ABC=x°$, then find the value of $x$.