Question: A regular pentagon is inscribed in a circle. If A and B are adjacent vertices of the pentagon and O is the center of the circle, what is the value of ∠OAB ?
- 48 degrees
- 54 degrees
- 72 degrees
- 84 degrees
- 108 degrees
“A regular pentagon is inscribed in a circle. If A and B are”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “The Official Guide for Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.
Solution and Explanation:
This question can be solved by only one approach.
Since it is mentioned that the pentagon is regular, hence its all the sides are equal. In the diagram attached, if you join the vertices of the pentagon with the centre, then you will get 4 isosceles triangles. Each triangle will have a central angle i.e. angle at the centre of the circle and two equal angles, both at the vertex of the pentagon.
So there will be 5 central angles. Name them as x. So as per the property of the circle, the sum of the entire central angle will be 360.
Hence 5x = 360 or x = 72.
It's now clear that the value of the central angle of each triangle will be 72. Therefore the sum of the rest of the angles will be
180−72=108
108 is the sum of two equal angles, hence each angle will be equal to 54.
The value of the angle OAB is 54.
Correct Answer: B
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