Confusing interior and exterior angle formulas
"The Inside-Out Error"
The Mistake in Action
Find the size of each interior angle of a regular pentagon.
Wrong: $\frac{360°}{5} = 72°$
Why It Happens
Students use $\frac{360°}{n}$, which gives the exterior angle, not the interior angle.
The Fix
$\frac{360°}{n}$ gives the EXTERIOR angle.
For the INTERIOR angle of a regular polygon, either:
Method 1: Calculate interior directly $$\text{Interior angle} = \frac{(n-2) \times 180°}{n} = \frac{3 \times 180°}{5} = \frac{540°}{5} = 108°$$
Method 2: Find exterior first, then subtract from 180° $$\text{Exterior} = \frac{360°}{5} = 72°$$ $$\text{Interior} = 180° - 72° = 108°$$
Spot the Mistake
Can you identify where this student went wrong?
Find each interior angle of a regular pentagon.
Interior angle $= \frac{360°}{5} = 72°$
Click on the line that contains the error.
Related Topics
Learn more about the underlying maths: