Angle sum + Interior and exterior angles

Angle sum of Triangles

The rule: In any triangle, the three interior angles always add up to a straight line, which is 180

Angle sum of quadrilateral

The angle sum of any quadrilateral is always 360. This is because a quadrilateral can be divided into two triangles, and the sum of the interior angles of each triangle is 180. Therefore,

180∘+180∘=360∘

Interior Angles

The angles inside a polygon.

Exterior Angles

Angles formed outside a polygon by one side and the extension of an adjacent side.

Interior and Exterior on a Straight Line

An interior angle and its corresponding exterior angle on a straight line always add up to 180∘.

Formula: Exterior Angle=180∘−Interior Angle.

Sum of Exterior Angles

The sum of the exterior angles of any polygon is always 360∘

Exterior Angle of a Triangle

The exterior angle of a triangle is equal to the sum of the two opposite interior angles.

Formula: Exterior Angle=Interior Angle 1+Interior Angle 2

Regular Polygons

For a regular polygon, the size of one exterior angle can be found by dividing 360∘by the number of sides.

Formula: Exterior Angle=360∘Number of sides

Co-interior angles

Angles on the same side of a transversal intersecting parallel lines, which add up to 180∘

Alternate angles

Angles on opposite sides of the transversal, which are equal if the lines are parallel.

Corresponding angles:

Angles in the same position at each intersection, which are equal if the lines are parallel.