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, PQRS is a square of side 2 cm and PLMN is a rectangle. The corner L of the rectangle is on the side QR. Side MN of the rectangle passes through the corner S of the square.
What is the area (in cm²) of the rectangle PLMN?
Note: The figure shown is representative.
A regular dodecagon (12-sided regular polygon) is inscribed in a circle of radius $r$ cm as shown in the figure. The side of the dodecagon is $d$ cm. All the triangles (numbered 1 to 12) in the figure are used to form squares of side $r$ cm and each numbered triangle is used only once to form a square.
The number of squares that can be formed and the number of triangles required to form each square, respectively, are:
Note: The figure shown is representative.
- Which one of the following options has the correct sequence of objects arranged in the increasing number of mirror lines (lines of symmetry)?
- A circle with center at $(x, y) = (0.5, 0)$ and radius $= 0.5$ intersects with another circle with center at $(x, y) = (1, 1)$ and radius $= 1$ at two points. One of the points of intersection $(x, y)$ is:
- During a half-moon phase, the Earth-Moon-Sun form a right triangle. If the Moon-Earth-Sun angle at this half-moon phase is measured to be $89.85^{\circ}$, the ratio of the Earth-Sun and Earth-Moon distances is closest to
