Question

If a regular polygon has 10 sides, then the measure of its each interior angle is ___.

• A. 150
• B. 162
• C. 144
• D. 120

Answer 1

The correct option is C 144

Each exteior angle (e°) = $\frac{360°}{n}$, where n is the number of sides of a polygon.
Each exteior angle (e°) = $\frac{360°}{10}$
Each exteior angle (e°) = 36
We know, in ar regular polygon each interior angle (i°) + exterior angle (e°) = 180°
i° + 36° = 180°
Hence i° = 144°
Alternative Method:
Sum of interior angles of a polygon = (n -2) x 180 where n is the number of sides of the polygon:
Hence $(10-2)\times 180=8\times 180={1440}^{\circ }$.
Since it is a regular polygon, all interior angles will be equal.
Hence Each interior angle = $\frac{Sumofinteriorangles}{n}$ = $\frac{1440}{10}$ = ${144}^{\circ }$