Premium Online Home Tutors
3 Tutor System
Starting just at 265/hour
Answer :
(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.