Properties of Triangles

Find the value of unknown $x$ in the following.

In the figure $ABCDE$, $\angle 1+\angle 2+\angle 3+\angle 4+\angle 5$.

Draw $△\mathrm{ABC}$ and form an exterior $\angle \mathrm{ACD}$. Now take a protractor and measure $\angle \mathrm{ACD}, \angle \mathrm{A} \text{and} \angle \mathrm{B}$.

Find the sum of $\angle \mathrm{A}+\angle \mathrm{B}$ and compare it with the measure $\angle \mathrm{ACD}$

Do you observe that $\angle \mathrm{ACD}$ is equal or nearly equal to $\angle \mathrm{A}+\angle \mathrm{B}$.

In the figure find the values of $x$ and $y$.

One of the exterior angle of a triangle is $105°$, and the interior opposite angles are in the ratio $2:5$. Find the angles of the triangle. 

If an exterior angle of a triangle is $130°$, and one of the interior opposite angles is $60°$. Find the other interior opposite angle. 

The exterior $\angle PRS$of $△PQR$ is $105°$ If $Q=70°$, find $\angle P$. Is $\angle PRS>\angle P$? 

One of the exterior angles of a triangle is $125°$ and the interior opposite angles are in the ratio $2:3$. Find the angles of the triangle. 

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

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

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

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

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

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

In the figure $\angle BAD=3\angle DBA$ find $\angle CDB, \angle DBC \text{and} \angle ABC$.

In the following figure, find the values of $x$ and $y$.

In the following figure, find the values of $x$.

Find the measure of angles $x$ and $y$.

For $△ABC$, find the measure of $\angle ACD$.

In $△ABC$, name all the interior and exterior angles of the triangle.