Learn how to account the admeasurement of the autogenous angles of a approved polygon, such as a pentagon.
This assignment includes:
Created in affiliation with GCSEPod
A polygon is a two-dimensional (2D) appearance amid by three or added beeline lines. 2D agency the appearance is flat, so it can be fatigued on paper.
Polygons can be approved or irregular. A approved polygon is a 2D appearance which has all abandon of the aforementioned breadth and all angles that are the aforementioned size.
The autogenous angles of a polygon are the angles that are central the shape.
By alive that the autogenous angles in a triangle add up to 180°, you can account the autogenous bend sum of added polygons.
This can again advice you to acquisition the admeasurement of every autogenous bend in a approved polygon.
One way to acquisition the sum of the autogenous angles of a polygon is to bisect the polygon into triangles.
Choose one vertex, or corner, of the polygon and draw beeline curve abutting this acme to all of the added vertices. This will bisect the central of the polygon into a cardinal of triangles.
To acquisition the absolute of the autogenous angles you accumulate the cardinal of triangles by 180°.
Example 1 – Approved pentagon
The pentagon (5-sided shape) aloft can be breach into 3 triangles. To acquisition the sum of the autogenous angles, you accumulate 3 by 180°.
Interior bend sum of a pentagon = 3 x 180° = 540°
If the polygon is approved – all its autogenous angles are according – you can use the aftereffect of the bend sum aloft to account the admeasurement of anniversary angle.
To do this, bisect the sum of the autogenous angles by the cardinal of autogenous angles.
In the archetype above, you would bisect 540° by 5, because there are 5 appropriately sized autogenous angles in a approved pentagon.
Therefore, the autogenous bend admeasurement of a approved pentagon = 540° ÷ 5 = 108°
Example 2 – Approved 20-sided polygon
When you bisect a polygon into triangles, the cardinal of triangles is consistently 2 beneath than the cardinal of sides.
To account the admeasurement of anniversary bend in a approved 20-sided polygon you charge to acquisition the sum of the autogenous angles first:
(20 – 2) x 180° =
18 x 180° =
This agency that all of the autogenous angles of any 20-sided polygon add up to 3240°.
To acquisition the admeasurement of anniversary autogenous bend you bisect this sum by 20:
3240° ÷ 20 = 162°
Find the autogenous angles of a approved polygon
Put what you accept abstruse about autogenous angles of approved polygons to the analysis by accepting a go at the tasks in this worksheet from GCSEPod.
Task 2 requires you to assignment logically – use what you apperceive about the autogenous bend ethics of the two shapes in anniversary aggregate to assignment out the final amount you need.
Click actuality for the acknowledgment sheet.
Have a attending at these added assets about the BBC and the web.
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