Question

In the figure an equilateral triangle, a square, a regular hexagon are put together
a) what is the measure of the inner angles of a polygon
b) find angle ABC
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Answer 1

Given : in figure an equilateral triangle, a square, a regular hexagon are put together

To Find : a) what is the measure of inner angles of each polygon?

B) find ∠ABC

Value of S

Solution:

Inner angle of a Regular polygon   = (n-2)180° / n

Inner angle of equilateral triangle  = (3 - 2) 180° / 3 =  60°

Inner angle of Square  = (4 - 2) 180° / 4 =  90°

Inner angle of regular Hexagon  = (6 - 2) 180° / 6 =  120°

∠ABC = Angle of Square + angle of Equilateral triangle

= 90° + 60°

= 150°

∠S = 360° - ( Angle of Square + angle of Equilateral triangle + angle of regular Hexagon )

=>  ∠S = 360° - ( 90° + 60° + 120° )

=>  ∠S = 360° - ( 270° )

=>  ∠S = 90°

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