Please enter the following details
Free Daily Targets & Mocks
Study Material & Formulas PDFs
1 on 1 Mentorship
Question 63
In a regular polygon, any interior angle exceeds the exterior angle by 120 degrees. Then, the number of diagonals of this polygon is
Correct Answer: 54
Solution
The sum of the interior angles of a polygon of 'n' sides is given by $$\left(2n-4\right)\times\ 90$$, and the sum of the exterior angles of a polygon is 360 degrees.
So, the difference between them will be 120 * n
=> $$\left(2n-4\right)90-360=120n$$
=> 60n = 720 => n = 12.
We know that the number of diagonals of a regular polygon is nC2 - n = 12C2 - 12 = 66 - 12 = 54.
Video Solution
Create a FREE account and get:
- All Quant CAT complete Formulas and shortcuts PDF
- 38+ CAT previous year papers with video solutions PDF
- 5000+ Topic-wise Previous year CAT Solved Questions for Free
CAT Quant Questions | CAT Quantitative Ability
CAT Linear Equations QuestionsCAT Mensuration QuestionsCAT Time And Work QuestionsCAT Logarithms QuestionsCAT Percentages Questions
CAT DILR Questions | LRDI Questions For CAT
CAT Venn Diagrams QuestionsCAT Puzzles QuestionsCAT Games and Tournamnents QuestionsCAT Data Interpretation QuestionsCAT Truth Lie Concept Questions
