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
- The adjacent sides of a parallelogram are $4a$ and $3a$. If the angle between them is $60^{\circ}$, then one of the diagonals of the parallelogram will be:
- Every interior angle of a regular octagon is $135^\circ$. Find the exterior angle of the octagon.
- PQ is a diameter of circle whose centre is O. If a point R lies on a circle and $\angle RPO$ is $42^\circ$, then find $\angle RQP$.
- ABC is an equilateral triangle and O is its circumcentre. If the side of triangle is 6 cm, then the $\angle BOC$ is:
- If every interior angle of a regular polygon is $144^\circ$, then the polygon has ______ sides.
- The ratio of the numbers of sides of two regular polygons is $1 : 2$. If each interior angle of the first polygon is $140^\circ$, then the measure of each interior angle of the second polygon is:
- 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 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 area of an isosceles right angle triangle is $81 \text{ cm}^2$ . Find the length of its hypotenuse.
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.
