Polygon Interior Angle Calculation
The question asks for the measure of an interior angle of a regular polygon with 10 sides.
Interior Angle Formula
For any regular polygon with $n$ sides, the formula to calculate the measure of each interior angle is:
$ \text{Interior Angle} = \frac{(n-2) \times 180^\circ}{n} $
Applying the Formula
In this case, the polygon has 10 sides, so $n = 10$. Plugging this value into the formula:
- Substitute $n=10$:
$ \text{Interior Angle} = \frac{(10-2) \times 180^\circ}{10} $
- Simplify the expression:
$ \text{Interior Angle} = \frac{8 \times 180^\circ}{10} $
- Calculate the result:
$ \text{Interior Angle} = \frac{1440^\circ}{10} $
$ \text{Interior Angle} = 144^\circ $
Conclusion
Therefore, the interior angle between the sides of a regular polygon with 10 sides is 144 degrees.
Important Questions from Mensuration and Geometry
In the given figure, $P, Q$, and $R$ are three points on a circle of radius 10 cm with $O$ as its center, $\overline{PQ} = \overline{RQ}$, and $\angle PQR = 45^\circ$. The figure is representative.
The area of the shaded region $PQRO$ is ______________ cm$^2$.
- A straight line $y = x - 1$ intersects a circle with center at $x = 1, y = 1$ and radius of magnitude 1 at two points. The length of the chord formed by this intersection is _______. (rounded off to three decimal places)
- The shell of a hollow spherical nanoparticle has a uniform thickness of 3 nanometers (nm). The outer radius of the nanoparticle is 5 nm. The ratio of the volume of the shell to the volume of the hollow core is ________
(Round off to one decimal place) - The volume of a sphere of diameter 1 unit is ______ than the volume of a cube of side 1 unit.
- A window is made up of a square portion and an equilateral triangle portion above it. The base of the triangular portion coincides with the upper side of the square. If the perimeter of the window is 6 m, the area of the window in $m^2$ is ______
