Bissoy.com
Doctors Medicines MCQs Q&A

If the difference between interior and exterior angle of a regular polygon is 60° then what is the sum of interior angles of the polygon?

If the difference between interior and exterior angle of a regular polygon is 60° then what is the sum of interior angles of the polygon? Correct Answer 720°

Let interior and exterior angle of polygon be I and E respectively. Then,

I - E = 60°      ----(1)

∵ The sum of interior and exterior angle is 180° ∴ I + E = 180°       ----(2)

Solving (1) and (2) for I and E,

⇒ I = 120° and E = 60°

Let n be the number of sides of polygon.

∴ 60° × n = 360° (∵ sum of exterior angles of any regular polygon is 360°)

⇒ n = 6

∴ sum of interior angles = (n - 2) × 180° = (6 - 2) × 180° = 720° 

Related Questions

Consider the following statements: (1) If n ≥ 3 and m ≥ 3 are distinct positive integers, then the sum of exterior angles of a regular polygon of m sides is different from the sum of exterior angles of regular polygon of n sides (2) Let m, n be integers such that m > n ≥ 3. Then the sum of the interior angles of regular polygon of sides is greater than the sum of interior angles of a regular polygon of n sides, and their sum is (m + n)π/2 Which of the above statements is/are correct?
Which of the following statement(s) given below is / are TRUE? A: Sum of exterior angle of triangle is less than the sum of exterior angle of a quadrilateral. B: Sum of interior angles of a polygon is (n - 1) × 90° (‘n’ is number of sides.) C: Interior angle of regular polygon is 72°, then measure of its corresponding exterior angle is 108°. 
The number of sides of polygon A is 6 more than the number of sides of polygon B. Interior angle of polygon A is 10° more than the interior angle of polygon B. Find the interior angle of polygon whose side is equal to sum of number of sides of polygon A and B.
Consider the following statements. A) A regular polygon whose exterior angle between 75° and 85°. B) Ratio of interior angle to exterior angles having 5 sides of a polygon is 3 : 2. C) A polygon whose number of diagonals is 7. Which statement(s) is/are true?
The sum of interior angle of a regular polygon is twice the sum of its exterior angles. Find the sum of interior angle of the polygon.
The sum of the interior angles of a regular polygon is 2340°. What is the difference between an interior angle and an exterior angle of the polygon?
The sum of the interior angles of a regular polygon is 1260°. What is the difference between an exterior angle and an interior angle of the polygon?
The sum of interior angle of a regular polygon is 1800°. What is the difference between an interior and an exterior angle of the regular polygon?
Find the regular polygon whose interior angel is 150 more than exterior angle. note the total sum of interior and exterior angle should be 180 at one point ?
March List I with List II :   List I   List II (A) Supplementary angles (I) Angles less than 90° (B) Complementary angles (II) Two angles whose sum is 180° (C) Acute angles (III) Angles greater than 90° but less than 180° (D) Obtuse angles (IV) Two angles whose sum is 90° Choose the correct answer from the options given below :