If a star figure is formed by elongating the sides of a regular pentagon then the measure of each an...........

Quantitative Aptitude (CDS) Mensuration 2D

If a star figure is formed by elongating the sides of a regular pentagon, then the measure of each angle at the angular points of the star figure is

36^o

35^o

32^o

30^o

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Explanation:

Measure of each interior angle of the regular pentagon
=(5-2) x 180^o/5=540^o/5=108^o
∠BCJ = ∠CBF = 108°
∴ ∠ACB = ∠ABC
=180°−108°=72°
Using angle sum property in ?ABC,we have
∠A=180°−(∠ACB+∠ABC)
=180°−(72°+72°)
=180°−144=36°
Thus, the measure of each angle at the angular points of the star figure is 36°.