### Edexcel GCSE Maths

Numbers
Algebra
Geometry and Measures
Probability
Statistics

# Types of angles

An angle is a figure formed when two rays meet, known as the sides of the angle, sharing a common endpoint called the vertex. Angles are used to measure the space between the two rays and are usually measured in degrees (°).

The main types of angles are:

• Acute anglesmeasure greater than 0° and less than 90°
• Right anglesmeasure exactly 90°
• Obtuse angles – measure greater than 90° and less than 180°
• Straight angles – measure exactly 180°
• Reflex angles – measure greater than 90° and less than 180°
• Complete angles – also known as complete angles, measure exactly 360°

## Pairs of Angles

Three different pairs of angles are:

• Complementary angles
• Supplementary angles
• Vertically opposite angles

Complementary angles are two angles which add up to 90°. If one angle is known, the other can be found by subtracting it from 90°. For example, if one angle is 30°, its complementary angle is 60°, as 30° + 60° = 90°.

Supplementary angles are two angles which add up to 180°. If one angle is known, the other can be found by subtracting it from 180°. For example, if one angle is 120°, its supplementary angle is 60°, as 120° + 60° = 180°.

Vertically opposite angles are formed when two straight lines intersect each other, creating pairs of equal angles opposite each other. For example, if two lines intersect and create an angle of 40°, the vertically opposite angle will also be 40°.

## Drawing Accurate Angles

1. Draw a horizontal line

Begin by drawing a straight horizontal line. Label the two endpoints with consecutive letters, such as Q and R.

2. Place the protractor and measure the desired angle.

Place the centre of the protractor on one of the endpoints, for example, point A. Ensure the base of the protractor is aligned with the line segment AB. After this, locate the desired angle measurement on the protractor scale, such as 60°.

3. Mark the angle, then draw it.

Make a small mark at the 60° point on the protractor’s edge. Then, move the protractor and draw a line segment from point A to the mark you made for 60°. Label the new point with another letter, such as C.

Now, you have successfully drawn an angle of 60° at point A, between line segments AB and AC.