Types of Angles

In the adjoining figure, $OQ$ bisects $\angle AOB$. $OP$ is a ray opposite to ray $OQ$. Prove that $\angle POA=\angle POB$.

Two adjacent angles are equal. Is it necessary that each of these angles will be a right angle? Justify your answer.

All linear pairs are supplementary angles whereas all supplementary angles are not linear pairs.

In figure given below, lines $AB$ and $CD$ intersect each other at the point $O$. If $\angle AOC=45°$, find the values of $x,y \text{and} z$.

In figure given below, ray $OC$ stands on line $AB$ and $4x-3y=20$. Find the measures of $\angle BOC$ and $\angle AOC$.

The sum of angles at a point on one side of a line is equal to _____ right angles. (one/ two/ three)

In the following figure, $AB$ and $CD$  are two straight lines which intersect each other at the point $O$. Find the values of $x, y$ and $z$.

In the following figure, lines $AB$ and $CD$ intersect each other at $O$. Find the values of $x, y$ and $z$.

Find the values of $x, y$ and $z$ in the following figure:

Find the values of $x, y$ and $z$ in the following figure:

If non-common arms of adjacent angles form a line, then the adjacent angles are said to form _____. 

In the adjoining figure, if $x+y=z+w$, then prove that $AOB$ is a straight line.

In the adjoining figure, $\angle AOC$ and $\angle BOC$ form a line $AB$. If $a-b=80°$, find the values of $a$ and $b$.

In the adjoining figure, $OD$ is the bisector of $\angle AOC$, $OE$ is the bisector of $\angle BOC$ and $OD\perp OE$. Show that the points $A, O$ and $B$ are collinear.

In the adjoining figure, for what value of $x+y$ will $ABC$ a straight line. Justify your answer. 

In the adjoining figure, $AOB$ is a straight line. Find the value of $x$. 

Two angles measure$\left(30°-x\right)$ and $\left(125°+2x\right)$. If each angle is the supplement of the other, find the angles. 

Find the angle which is one fifth of its complement.

If two lines intersect each other, then the vertically opposite angles are _____. (equal / unequal / different)

The sum of all the angles (drawn at a plane) at a point is _____$°$.