Yes, it is possible to construct a polygon where the sum of its interior angles is 20 right angles. Here's a detailed, step-by-step solution to find the number of sides of such a polygon:
1. Understand the given information:
- The sum of the interior angles of the polygon is 20 right angles.
2. Convert right angles to degrees:
- We know that 1 right angle = 90 degrees.
- Therefore, 20 right angles = 20 * 90 degrees = 1800 degrees.
3. Use the formula for the sum of the interior angles of a polygon:
- The formula to calculate the sum of the interior angles of a polygon with [tex]\( n \)[/tex] sides is given by:
[tex]\[
(n - 2) \times 180 \text{ degrees}
\][/tex]
4. Set up the equation:
- We know from the given information that the sum of the interior angles is 1800 degrees. So, we can set up the equation as:
[tex]\[
(n - 2) \times 180 = 1800
\][/tex]
5. Solve for [tex]\( n \)[/tex]:
- Divide both sides of the equation by 180 to isolate [tex]\( n - 2 \)[/tex]:
[tex]\[
n - 2 = \frac{1800}{180}
\][/tex]
- Simplify the right side of the equation:
[tex]\[
n - 2 = 10
\][/tex]
- Add 2 to both sides to solve for [tex]\( n \)[/tex]:
[tex]\[
n = 10 + 2
\][/tex]
[tex]\[
n = 12
\][/tex]
6. Conclusion:
- Therefore, the polygon with the sum of its interior angles equal to 20 right angles (1800 degrees) has 12 sides.
Hence, it is possible to construct such a polygon, and it is a dodecagon (12-sided polygon).
