# CAT Quantitative Aptitude Questions | Geometry Questions for CAT - Triangles

###### CAT Questions | CAT Geometry Questions | Regular Polygon

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°

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##### 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.

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