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In the following figure, a regular hexagon, a regular pentagon and an equilateral triangle given, then, find the value of ∠GCH?

In the following figure, a regular hexagon, a regular pentagon and an equilateral triangle given, then, find the value of ∠GCH? Correct Answer 72°

CONCEPT USED:

Each interior angle of a polygon = /n, where, n is the number of sides.

CALCULATION:

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Each interior angle of hexagon, ABCDEF = (6 – 2) × 180°/6 = 120°

Each interior angle of pentagon, CHIJD = (5 -2)× 180°/5 = 108°

Each interior angle of triangle, BCG = 60°

In the figure,

∠BCD = 120°, ∠DCH = 108°, ∠BCG = 60°

We know that the sums angles around a point is 360°

⇒ ∠BCD + ∠DCH + ∠BCG  +∠GCH = 360°

⇒ 120° + 108° + 60° + ∠GCH = 360°

⇒ 288° + ∠GCH = 360°

⇒ ∠GCH = 360° - 288°

⇒ ∠GCH = 72°

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