Angle Basics

An angle is formed by two rays with the same endpoint.
A ray is a part of a line that has one endpoint and goes on indefinitely in one direction.
Angles are measured in degrees (°). A complete circle is divided into 360°.

An angle that measures exactly 90° is called a right angle.
An angle that measures less than 90° is called an acute angle.
An angle that measures more than 90° but less than 180° is called an obtuse angle.
An angle that measures exactly 180° is called a straight angle.

Adjacent angles are two angles that have a common vertex and a common arm. The other arms of the angles are on opposite sides of the common arm.
Vertical angles are angles opposite each other when two lines intersect. They are always equal.
Supplementary angles are two angles that add up to 180°. They form a straight line.
Complementary angles are two angles that add up to 90°.
When a line crosses two parallel lines, the alternate angles are equal, the corresponding angles are equal and the co-interior angles add up to 180°.

The angles in a triangle always sum up to 180°.
The angles in a quadrilateral always sum up to 360°.
To find the sum of the interior angles of a polygon, use the formula (n - 2) × 180°, where ‘n’ is the number of sides in the polygon.
The exterior angles of any polygon always add up to 360°.

The angle at the centre of a circle is twice the angle at the circumference on the same arc.
The angle in a semi-circle is 90°.
Angles in the same segment are equal.
Opposite angles of a cyclic quadrilateral add up to 180°.
The exterior angle of a cyclic quadrilateral is equal to the interior opposite angle.