Question 97

If a regular polygon has 5 sides then the measure of its interior angle is greater than the measure of its exterior angle by how many degrees?

Solution

Sum of interior angles of a regular polygon = $$(n-2)\times180^\circ$$

Sum of all interior angles of a pentagon = $$(5-2)\times180^\circ=540^\circ$$

=> Measure of an interior angle of a polygon = $$\frac{540}{5}=108^\circ$$

Sum of all exterior angles of a pentagon = $$360^\circ$$

=> Measure of an exterior angle of a polygon = $$\frac{360}{5}=72^\circ$$

$$\therefore$$ Required difference = $$108^\circ-72^\circ=36^\circ$$

=> Ans - (B)


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