Calculating Interior Angle Sum for a 20-Sided Polygon
The sum of the interior angles of a polygon with n sides can be found using a specific formula.
Interior Angle Sum Formula
The formula to calculate the sum of all interior angles ($S$) of an $n$-sided polygon is:
$ S = (n-2) \times 180^\circ $
Applying the Formula
In this question, we have a polygon with 20 sides. So, $n = 20$. Substitute this value into the formula:
- $n = 20$
Calculation Steps
Calculate the sum using the formula:
- Subtract 2 from the number of sides: $n - 2 = 20 - 2 = 18$.
- Multiply the result by $180^\circ$: $18 \times 180^\circ$.
- Perform the multiplication: $18 \times 180^\circ = 3240^\circ$.
Therefore, the sum of all interior angles of a 20-sided polygon is $3240^\circ$.
Conclusion
Comparing the result with the given options, the correct answer is $3240^\circ$.
Similar Questions
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Important Questions from Geometry
ABCDEF is a regular hexagon. Side of the hexagon is 36 cm. What is the area of the triangle AOB ?
If ∆ABC ~ ∆DEF, and BC = 4 cm, EF = 5 cm and the area of triangle ABC = 80 cm 2, then the area of the triangle DEF is:
If Δ ABC is right angled at B, AB = 12 cm and ∠CAB = 60°, determine the length of BC.
If ΔABC and ΔDEF are congruent triangles, then which of the following is FALSE?
D and E are points on the sides AB and AC, respectively, of ΔABC such that DE is parallel to BC and AD ∶ DB = 7 ∶ 9. If CD and BE intersect each other at F. then find the ratio of areas of ΔDEF and ΔCBF.
