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ABCDE is a regular pentagon. O is a point inside the pentagon such that AOB is an equilateral triangle. What is ∠OEA?
  • a)
    72°
  • b)
    54°
  • c)
    66°
  • d)
    48°
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
ABCDE is a regular pentagon. O is a point inside the pentagon such th...
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°
Hence, the correct option is (c).
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Most Upvoted Answer
ABCDE is a regular pentagon. O is a point inside the pentagon such th...
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°
Hence, the correct option is (c).
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ABCDE is a regular pentagon. O is a point inside the pentagon such that AOB is an equilateral triangle. What is ∠OEA?a)72°b)54°c)66°d)48°Correct answer is option 'C'. Can you explain this answer?
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