Join 60,000+ competitive exam aspirants
or with email
Your Cart
Subtotal₹0
Total₹0
Examoogle • User • info@examoogle.com • EE-2024-8821
Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked
Join 60,000+ competitive exam aspirants
If an exterior angle of a regular polygon is 40°, then find the number of diagonals of the polygon.
27
40
35
45
27
Calculate number of sides as 360/40=9, then quickly compute diagonals using (9×6)/2=27.
Exterior angle of a regular polygon = 40°. Total sum of exterior angles of any polygon = 360°.
n = \frac{360°{\text{Exterior Angle}}, D = \frac{n(n-3)}{2}
Calculate number of sides as 360/40=9, then quickly compute diagonals using (9×6)/2=27.
Students often confuse the number of sides n with the number of diagonals and stop after finding n=9.
Calculate the number of sides
Since the sum of exterior angles is always 360°, the number of sides n is given by 360/40.
n = \frac{360°{40° = 9
Apply the diagonal formula
The number of diagonals D in a polygon with n sides is given by the formula 2n(n−3).
D=29(9−3)
Final Calculation
Substitute n=9 into the formula to find the final count.
D=29×6=27
A is correct because calculating the sides gives n=9 and applying the diagonal formula yields 27.
This concept is closely linked to interior angle sum formulas: (n−2)×180°, which is often used in coordinate geometry and trigonometry questions.
Get instant step-by-step AI explanations, full shift Previous Year Papers (SSC GD, RRB, SSC JE), and regional rank analysis on the official Examoogle App.
Free Download • 100K+ Aspirants