Question : 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?
Option 1: $60^{\circ}$
Option 2: $36^{\circ}$
Option 3: $90^{\circ}$
Option 4: $100^{\circ}$
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Correct Answer: $36^{\circ}$
Solution : Sides of a pentagon, $n$ = 5 Each interior angle of a pentagon = $(\frac{2×5-4}{5})×90^{\circ}$ = $6 × 18^{\circ}$ = $108^{\circ}$ External angle of a pentagon = $\frac{360^{\circ}}{5}$ = $72^{\circ}$ Difference = $108^{\circ}$ – $72^{\circ}$ = $36^{\circ}$ Hence, the correct answer is $36^{\circ}$.
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