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

###### CAT Questions | CAT Geometry Questions | Polygons

The question is from the topic polygons. It discusses about the angles formed by diagnols in a polygon.CAT Geometry questions are heavily tested in CAT exam. Make sure you master Geometry problems.

Question 45: The number of sides in a regular polygon is ‘T’ times the number of diagonals in it. What is the interior angle of this polygon in terms of T?

1. 180 * $$frac{$T+2$}{(3T+2)}$ 2. 540 * $\frac{$T+2$}{(3T+2)}$ 3. 360 * $\frac{$T+2$}{(3T+2)}$ 4. 90 * $\frac{$T+2$}{(3T+2)}$ ## Best CAT Online Coaching Try upto 40 hours for free Learn from the best! #### 2IIM : Best Online CAT Coaching. ## Best CAT Coaching in Chennai #### CAT Coaching in Chennai - CAT 2022Limited Seats Available - Register Now! ### Explanatory Answer ##### Method of solving this CAT Question from polygons: Knowing the relationship between number of sides and diagonals of a polygon would be useful. Let the number of sides in the regular polygon be n. Therefore, Number of diagonals = nC2 - n = $\frac{n$n-1$}{2}$ - n = $\frac{n^2-3n}{2}\\$ Given, Number of sides = p x Number of diagonals => n = T * $\frac{n^2-3n}{2}\\$ => n = $\frac{2}{T}\\$ + 3 Interior angle =$n-2) * $$frac{180}{n}\\$ + 3 =$$$frac{2}{T}\\$+ 3 - 2) * $\frac{180}{2/T + 3}\\$ =$$$frac{2}{T}\\$ + 1) * $\frac{180}{2/T + 3}\\$ = 180 * $\frac{$T+2$}{(3T+2)}$ The question is " What is the interior angle of this polygon in terms of T?" ##### Hence, the answer is 180 * $\frac{$T+2$}{(3T+2)}$ Choice A is the correct answer. ###### Best CAT Online Coaching Try upto 40 hours for free Learn from the best! ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2024 Classroom Batches Starting Now! @Gopalapuram ###### Best CAT Coaching in Chennai Introductory offer of 5000/- Attend a Demo Class ###### Best Indore IPM & Rohtak IPM CoachingSignup and sample 9 full classes for free. Register now! ## CAT Preparation Online | CAT Geometry questions Videos On YouTube #### Other useful sources for Geometry Question | Geometry Triangles Circles Quadrilaterals Sample Questions ##### Where is 2IIM located? 2IIM Online CAT Coaching A Fermat Education Initiative, 58/16, Indira Gandhi Street, Kaveri Rangan Nagar, Saligramam, Chennai 600 093 ##### How to reach 2IIM? Phone:$91) 44 4505 8484
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