# Angle Properties – O Level Exam Preparation Guide

In this revision note, you will learn the all the angle properties and applying them to solve Geometry questions on Polygons.

## Different types of angles

a) An **acute** angle is less than 90°.

b) A **right** **angle** is equal to 90°.

c) An **obtuse** angle is between 90° and 180°.

d) A **straight line** is equal to 180°.

e) A **reflex angle** is larger than 180° but less than 360°.

f) A **complete turn** is 360°

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## Angle Properties

1) Two angles are said to be **complementary angles** if their sum is 90°.

2) Two angles are called **supplementary angles** if their sum is 180°.

3) **Vertically opposite angles** are those on the opposite sides of two intersecting lines.

4) Two angles are said to be **corresponding angles** if they have the same relative positive at the each intersection where a line cuts across a pair of parallel lines.

The corresponding angles are equal to each other.

5) Two angles are called **alternate angles** if they lie on the different side of the line cutting across a pair of parallel lines.

The alternate angles are equal to each other.

6) Two angles are known as **interior angles** if they lie on the same side of the line that lie on the different side of the line cutting across a pair of parallel lines.

Interior angles add up to 180°.

## Angle Properties of Polygons

A **polygon** is a closed plane figure with three or more straight lines. Polygons are named according to the number of sides they have.

Note: Polygon with n sides is called an n-gon.

A **regular polygon** is a polygon with all its sides and angles equal.

## Angle Properties of Triangles

a) An **equilateral** **triangle** is a triangle with 3 equal sides. Each of its angles is 60°.

b) An **isosceles triangle** is a triangle with 2 equal sides. Its base angles are equal.

The **sum of the interior angles** of a triangle is always 180°.

## Angle Properties of Rhombus

- Opposite angles are equal (
*∠a = ∠a*) - ∠a + ∠b = 180° (Interior angles)

- The diagonals bisect the angles equally
- The diagonals intersect at Right Angles

## Angle Properties of Parallelogram

- Opposite angles are equal (
*∠a = ∠a )* *∠a + ∠b*= 180° (Interior angles)

- diagonals DO NOT bisect the angles equally
- diagonals DO NOT intersect at Right Angles

## Angle Properties of Trapezium

- ∠a + ∠d = 180° (interior angles formed between parallel lines)
- ∠b + ∠c = 180° (interior angles formed between parallel lines)
- ∠a + ∠d = ∠b + ∠c

## Sum of Angles in a Quadrilateral

A **quadrilateral** is a 4-sided polygon. Any quadrilateral can be divided into 2 triangles along its diagonal. Since the angles of a triangle add up to 180°, the angle sum of a quadrilateral is 180° × 2 = 360°.

## Sum of Interior Angles in a Polygon

A polygon with n sides has n interior angles.

The sum of interior angles = (n – 2) × 180°.

## Sum of Exterior Angles in a Polygon

A polygon with n sides has n exterior angles.

Each pair of interior angle and exterior angle is supplementary (add up to 180°).

The sum of the exterior angles of an n-sided polygon is always 360°

## Angle Properties of Polygons Example 1

Find the exterior angle of a 12-sided regular polygon.

Let *x* the size of each exterior angle.

12 × *x* = 360°

x° = 30°

## Angle Properties of Polygons Example 2

The ratio of an interior angle to an exterior angle of a regular n-sided polygon is 8 ∶ 1. How many sides does the polygon have?

Let 8a and a be the interior angle and the exterior angle at the same vertex respectively.

exterior angle + interior angle = 180° (adjacent ∠s on a straight line)

a + 8a = 180°

a = 20°

Sum of exterior angles = 360°

20°(n) = 360°

n = 18

∴ The polygon has 18 sides.

## Last Minute Revision for O Level Math?

## Check out our exam guide on other topics here!

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