Question 123

If ABCDEF is a regular hexagon, then ΔACE is

Solution

Sum of all angles of the hexagon = $$(n - 2) * 180^{\circ}$$

= (6-2)*180° = 720°

=> Each interior angle = $$\frac{720^{\circ}}{6}$$ = 120°

Since, AB = BC

=> $$\angle$$BAC = $$\angle$$ACB = 30°

=> $$\angle$$ACE = $$\angle$$CEA = $$\angle$$EAC = 60°

=> AC = CE = EA

=> $$\triangle$$ACE is an equilateral triangle.

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