Question 66

ABCDEFGH is a regular octagon inscribed in a circle with centre at O. The ratio of $$\angle$$OAB to $$\angle$$AOB is equal to:

Solution

ABCDEFGH is a regular octagon. So AB=BC=….. =HA

There are 8 equal angles AOB, BOC and so on formed, and AOB = $$\frac{360}{8}$$ = 45 degree

So in triangle AOB, sum of angles OAB and OBA is (180-45)=135 deg

Since side OA=OB

Angle OAB= Angle OBA = $$\frac{135}{2}=67.5^{\circ\ }$$

Angle AOB = 45$$^{\circ\ }$$

Required ratio = 67.5 : 45 = 3 : 2.

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