In the given figure, regular pentagons are drawn on each side of an equilateral triangle. Then find the measure of each angle between the pentagons. [4]
For a regular pentagon n=5
∴ Each exterior angle = 360∘5
=72∘ [1 mark]
Now, exterior angle + Interior angle = 180∘
⇒e+i=180∘
⇒72∘+i=180∘
⇒i=180∘−72∘
⇒i=108∘ [1 mark]
Also, each angle of an equilateral triangle = 60∘
Now, Angle about a point = 360∘
⇒108∘+60∘+108∘+x=360∘
⇒276∘+x∘=360∘
⇒x∘=360∘−276∘
⇒x∘=84∘
∴ Each angle between the pentagons is 84∘. [2 marks]