In the given figure, two straight lines AB and CD intersect at a point O such that $\angle AOC=50°.$ Find $\angle BOD$ and $\angle BOC$

In the given figure, $AOB$ is a straight line and $OC$ is a ray such that $\angle AOC=(3x+20)°$ and $\angle BOC=(2x-10)°$. Find the value of $x$ and hence find $\angle AOC$ and $\angle BOC$

In a $∆ABC,$ if $\angle A=65°$, $\angle B=45°$, find $\angle C$

In the given figure, $x:y=2:3 \text{and} \angle ACD=120°$. Find the values of $x, y$ and $z$.

In the adjoining figure, $ABC$ is a triangle in which $AD$ is the bisector of $\angle A$. If $AD\perp BC$, show that $△ABC$ is isosceles.