  # Calculating Angles at a Point and on a Straight Line

In this worksheet, students calculate angles at a point and on a straight line. Key stage:  KS 3

Curriculum topic:   Geometry and Measures

Curriculum subtopic:   Apply the Properties of Angles

Difficulty level:   #### Worksheet Overview

How do you feel about angles?  They're all around us if you think about it.  Why not take a look around and see how many you can see?

What's an angle?  An angle can be found anywhere that two straight lines meet.  It's the space in the middle of the two lines. Look at this pencil - the lead showing at the end could represent an angle for example!

To be able to feel confident when dealing with angles we need to learn a few key rules.  You can come back to this at any time, or, you may find it useful to write these down!

Rules of Angles

Angles at a point add to 360°, but what does this mean? Take a look below, you can see the point is where the two lines meet.  If we were to continue drawing around the whole point you will see that we've drawn a ... circle?  This leads us to our next rule...

Angles inside a circle add up to 360° it's a rule you just need to learn!

Angles on a straight line add to 180° this is a rule we just have to learn.  If you take a protractor to any straight line and measure the angle on it, you will find it always equals 180°, which is half the angle in a circle.

Have a look at the ways we can calculate angles below.

If we know one of the angles at a point, or on a straight line, we can calculate the other one based on the rules above.

Examples

At a point: - the angle adds up to 360 ° a + 270° = 360°
a = 90°

On a straight line: b + 65° = 180°
b = 115°

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