Formula sheet
Sum of interior angles of a polygon
(n − 2) × 180° is given on the exam formula sheet. You must still know that n is the number of sides, that the result is the total of all interior angles, and how to divide by n to get one angle of a regular polygon.
What the symbols mean
- n Number of sides (equal to the number of vertices/angles) of the polygon.
- 180° The angle sum of one triangle; the polygon is split into (n − 2) triangles.
Given in the exam, or memorise?
(n − 2) × 180° is given on the exam formula sheet. You must still know that n is the number of sides, that the result is the total of all interior angles, and how to divide by n to get one angle of a regular polygon.
Why it works
Any polygon can be cut into triangles from one corner.
- From one vertex, draw diagonals to every other vertex.
- An n-sided polygon splits into (n − 2) triangles this way.
- Each triangle has angles adding to 180°, so the total is (n − 2) × 180°.
Worked example 1
Find the sum of the interior angles of a hexagon (6 sides).
- Sum = (n − 2) × 180°, with n = 6
- = (6 − 2) × 180°
- = 4 × 180°
- = 720°
Worked example 2
Each interior angle of a regular polygon is 156°. How many sides does it have?
- Each interior angle = (n − 2) × 180° ÷ n
- 156 = (n − 2) × 180 ÷ n
- 156n = (n − 2) × 180 = 180n − 360
- 360 = 180n − 156n = 24n
- n = 360 ÷ 24 = 15
Where students go wrong
- Using (n − 2) × 180° for one interior angle: it gives the TOTAL; divide by n for one angle of a regular polygon.
- Confusing it with the exterior-angle sum, which is always 360° for any polygon.
- Miscounting the number of sides n (e.g. treating a pentagon as n = 4).
- Forgetting the −2 and writing n × 180°.
Use it with
Source:SPM: Format Pentaksiran mulai 2021, Matematik (1449)
Frequently asked questions
Do I need to memorise the polygon angle formula for SPM?
No. (n − 2) × 180° is printed on the SPM formula sheet.
Your job is to use it correctly: read n as the number of sides, and remember the answer is the sum of every interior angle. For a regular polygon you then divide that sum by n to get one angle.
How do I find one interior angle of a regular polygon?
First find the total with (n − 2) × 180°, then divide by n because a regular polygon has all angles equal. For example a regular octagon: (8 − 2) × 180° = 1080°, and 1080° ÷ 8 = 135°.
The two-step order, total first, then share out, is what most students slip on.
What is n in the formula?
n is simply the number of sides of the polygon, which equals its number of angles. A triangle is n = 3, a quadrilateral n = 4, a pentagon n = 5, and so on.
Count the sides carefully; putting the wrong n in is the most common cause of a wrong angle sum.