Premium Online Home Tutors
3 Tutor System
Starting just at 265/hour

# 5.(a) Is it possible to have a regular polygon with measure of each exterior angle a is $$22^{\circ}$$? (b) Can it be an interior angle of a regular polygon? Why?

(a) We have, Number of sides of regular polygon=$$\frac{360^{\circ} }{Exterior \;angle}$$

As we know number of sides by the formula should be an integer so, it is not possible that a regular polygon have its exterior angle of $$22^{\circ}$$ because $$22^{\circ}$$ is not divisible by $$360^{\circ}$$ hence, we can't get a whole number for calculating the number of side.

(b) If interior angle =$$22^{\circ}$$

And we have: measure of each interior angle=$$\frac{(n-2)\times180^o}n$$

$$\Rightarrow 180n -2 \times 180=22n$$

$$\Rightarrow 180n -22n=360$$

$$\Rightarrow 158n=360$$

$$\Rightarrow n=\frac{360}{158}$$

But 158 does not divide 360 exactly.So, the polygon is not possible.