Learn and use the actuality that exoteric angles in a polygon sum to 360°.
This assignment includes:
A polygon is a two-dimensional (2D) bankrupt appearance with at atomic 3 beeline sides. Polygons can be approved or irregular.
Regular polygons accept angles that are all according and abandon that are all according in length.
Irregular polygons can accept abandon of any breadth and angles of any size.
The exoteric bend at a acme (corner) of a appearance is fabricated by extending a side, represented in the diagram by the abject lines.
The sum of the exoteric angles of a polygon is 360°.
Imagine walking annular the alfresco of a polygon. By the time you acknowledgment to your starting point you will accept completed one abounding turn. Therefore all the corners of the polygon that you accept angry annular charge add to 360°.
Look at the diagram again, area the exoteric angles of the polygon accept been accustomed altered colours. You can see how they can be placed calm to anatomy a complete circle.
The sum of the exoteric angles of an aberrant polygon and of a approved polygon is 360°.
The blueprint for artful the admeasurement of an exoteric bend in a approved polygon is:
exterior bend of a polygon = 360 ÷ cardinal of sides
Remember that the exoteric bend added to the autogenous bend will add up to 180°, as they accommodated on a line.
Using these facts will advice you to assignment out bend problems apropos to polygons.
Example – Angles in a approved pentagon
How can you account the admeasurement of the exoteric and autogenous angles in a approved pentagon (a polygon with 5 according sides)?
Applying the facts aloft about angles in polygons, you can assignment out the following.
The sum of exoteric angles is 360°.
The exoteric bend is 360° ÷ 5 = 72°.
The exoteric and autogenous angles add up to 180° (notice the band they sit on in the diagram).
The autogenous bend is 180° − 72° = 108°.
Watch this abbreviate video from Pearson to see addition archetype of application polygon exoteric bend facts to assignment out a problem, this time with a approved decagon (a 10-sided polygon).
Interactive action – Exoteric angles
To get you beeline into practising your ability of angles in polygons, accept a go at this alternate action from MyMaths, Oxford University Press. Click on ‘Practice’ and alpha with Question 2, as this looks at the exoteric and autogenous angles of polygons, but if you would like analysis your added ability further, try Question 1 as well, which looks at angles in triangles.
Hint: the angles in a triangle add up to 180°. Angles that accommodated on a band additionally add up to 180°.
By auspicious the folio you can try altered versions of the questions. You can mark your answers aural the activity.
Sum of exoteric angles – skills
Now accept a go at this worksheet from White Rose Maths to put your compassionate of exoteric angles of polygons to the analysis – there are a ambit of problems to assignment through to get you thinking. Write your answers on a allotment of paper. If it helps you, you can account out the diagrams in the action application cardboard and a pencil.
Click actuality for the acknowledgment sheet.
Have a attending at these added assets about the BBC and the web.
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