CAT Practice : Geometry-Triangles

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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.

Regular pentagon

    Q.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 Answer
    Choice (A). 66°

Explanatory Answer

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Detailed Solution

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°
Answer choice (a)

Correct Answer: 66°

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Geometry is probably the most vital topic as far as CAT preparation is concerned. Geometry sets the stage for Trigonometry, Cogeo and Mensuration as well.