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The question is from regular polygon. It tests our understanding of angles in a regular polygon. CAT Geometry questions are heavily tested in CAT exam. Make sure you master Geometry problems. Triangles are heavily tested, the wonderful infinite-sided polygon that is the circle is also heavily tested. In between these two lies this great mass of regular polygons.

Question 8: ABCDE is a regular pentagon. O is a point inside the pentagon such that AOB is an equilateral triangle. What is ∠OEA?

1. 66^°
2. 48^°
3. 54^°
4. 72^°

Correct AnswerChoice A
66^°

Video Solution

Explanatory Answer

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Video Explanation

Explanatory Answer

Method of solving this CAT Question from Regular Polygon: Creating a new triangle by joining two existing ponits would help.

Join OE and OD.
Internal angle of regular pentagon = 108^°
∠EAB = ∠EDC = 108^°
∠OAB = 60^°
∠EAO = 48^°
AO = OB = AB as the triangle is equilateral.
AB = AE as this is a regular pentagon.

Triangle AEO is isosceles as AO = EA.
∠AEO = ∠AOE = x (say)

In triangle AEO,
∠OAE + 2x = 180^°
48^° + 2x = 180^°
2x = 132^°, or x = 66^°

The question is " What is ∠OEA?"
∠OEA = 66^°

Hence, the answer is 66^°

Choice A is the correct answer.