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Answer :

As we know that the sum of the exterior angles formed by producing the sides of a convex polygon in the same order is equal to 360°. Therefore here we have,

(a)\( x + 125^{\circ} + 125^{\circ} = 360^{\circ}\)

\(\Rightarrow x + 250^{\circ} = 360^{\circ}\)

\(\Rightarrow x = 360^{\circ}– 250° = 110^{\circ}\)

\(\Rightarrow x = 110^{\circ}\)

(b) \(x + 90^{\circ} +60^{\circ} + 90^{\circ} + 70^{\circ} = 360^{\circ} \)

\(\Rightarrow x + 310^{\circ} = 360^{\circ} \)

\(\Rightarrow x = 360^{\circ} – 310^{\circ} = 50^{\circ} \)

\(\Rightarrow x = 50^{\circ} \)

- 2.Find the measure of each exterior angle of a regular polygon of (i) 9 sides (ii) 15 sides
- 3.How many sides does a regular polygon have if the measure of an exterior angle is \(24^{\circ}\)?
- 4.How many sides does a regular polygon have if each of its interior angles is \(165^{\circ}\)?
- 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?
- 6.(a) What is the minimum interior angle possible for a regular polygon? Why? (b) What is the maximum exterior angle possible for a regular polygon?

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