# CAT Practice : Coordinate Geometry

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Geometry - Triangles

## Basic Geometry

Q.45: The number of sides in a regular polygon is â€˜Tâ€™ times the number of diagonals in it. What is the interior angle of this polygon in terms of T?
1. ${180 * \frac{(T+2)}{(3T+2)}}$
2. ${540 * \frac{(T+2)}{(3T+2)}}$
3. ${360 * \frac{(T+2)}{(3T+2)}}$
4. ${90 * \frac{(T+2)}{(3T+2)}}$

Choice (A). ${180 * \frac{(T+2)}{(3T+2)}}$

## Detailed Solution

Let the number of sides in the regular polygon be n.
Therefore, Number of diagonals = nC2 â€“ n = $\frac{n(n-1)}{2} - n = \frac{n^2 - 3n}{2}$
Given, Number of sides = p x Number of diagonals
=) $n = T * \frac{n^2 - 3n}{2}$
=) $n = \frac{2}{T} + 3$
Interior angle = $(n-2) * \frac{180}{n} + 3$
= $(\frac{2}{T} + 3 - 2) * \frac{180}{\frac{2}{T} + 3}$
= $(\frac{2}{T} + 1) * \frac{180}{\frac{2}{T} + 3}$
= ${180 * \frac{(T+2)}{(3T+2)}}$

Correct Answer: ${180 * \frac{(T+2)}{(3T+2)}}$

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## More questions from Geometry Triangles

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.