Exterior Angle of a Regular Octagon Calculation
To find the measure of each exterior angle of a regular octagon, we use the properties of polygons.
Key Concepts
- A regular polygon has all sides equal and all interior angles equal. Consequently, all exterior angles are also equal.
- The sum of the exterior angles of any convex polygon, one at each vertex, is always $360^\circ$.
Steps for Calculation
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Identify the type of polygon. The question refers to a regular octagon.
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Determine the number of sides ($n$) for the polygon. An octagon has $n = 8$ sides.
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Use the formula for calculating each exterior angle of a regular polygon:
Exterior Angle = $\frac{\text{Sum of Exterior Angles}}{n}$
Exterior Angle = $\frac{360^\circ}{n}$ -
Substitute the value of $n$ for an octagon into the formula:
Exterior Angle = $\frac{360^\circ}{8}$ -
Calculate the result:
Exterior Angle = $45^\circ$
Conclusion
Therefore, the measure of each exterior angle of a regular octagon is $45^\circ$. This matches Option A.
Similar Questions
- If the sum of the interior angles of a regular polygon is equal to four times the sum of its exterior angles, then what is the number of diagonals in the polygon?
- Find the ratio of the measure of an angle of a regular pentagon to that of a regular octagon.
- The area of an isosceles right angle triangle is $81 \text{ cm}^2$ . Find the length of its hypotenuse.
- In a polygon, the sum of the interior angles is triple the sum of the exterior angles. The number of sides is:
- The difference between the interior and exterior angles at a vertex of a regular polygon is $140^\circ$. The number of sides of the polygon is:
- The ratio of an interior angle to the exterior angle of a regular polygon is $4:1$. The number of sides of the polygon is:
- If the interior angles of a pentagon are in the ratio 1 : 3 : 5 : 7 : 11, then the measure of the smallest interior angle is:
- If the side of an equilateral triangle is 2 cm, then find the area and the altitude of the triangle.
- Two sides of a triangle are of lengths 4 cm and 10 cm. If the length of the third side is $a$ cm, then:
- If the difference between the interior and exterior angles of a polygon is $36^\circ$, then find the number of sides in the polygon.
Important Questions from Geometry
If the angles of a triangle are in the ratio of 2:3:4, then the difference of the measure of greatest angle and smallest angle is
In ΔABC, ∠A = 90°, AD ┴ BC and AD = BD = 2 cm. The length of CD is
How many lines of symmetry does a rectangle have?
The number of diagonals in each face a cube is
Which of the following is/are the geometric figures with the line of symmetry?
I. Rectangle
II. Isosceles triangle
