Question
Find the sum of 8 exterior angles of a 24-sided regular polygon.
The correct answer is
120°
Exterior Angles Sum Calculation
The sum of the exterior angles of any convex polygon is always 360°. For a regular polygon, all exterior angles are equal.
Calculating One Exterior Angle
A regular polygon with '$n$' sides has each exterior angle equal to $\frac{360^\circ}{n}$.
Given a polygon with 24 sides ($n = 24$), the measure of one exterior angle is:
Exterior Angle = $\frac{360^\circ}{24}$
Exterior Angle = $15^\circ$
Sum of 8 Exterior Angles
We need to find the sum of 8 exterior angles. Since all exterior angles are equal in a regular polygon:
Sum of 8 exterior angles = $8 \times (\text{measure of one exterior angle})$
Sum = $8 \times 15^\circ$
Sum = $120^\circ$
The sum of 8 exterior angles of a 24-sided regular polygon is 120°.
Was this answer helpful?
Important Questions from Geometry (Notes)
- Which of the following is not true for a parallelogram?
- A 6 cm long chord of a circle is at a distance of 4 cm from the centre of the circle. Find the distance of 8 cm long chord of the same circle from the centre.
- In a triangle PQR, if $\angle P + \angle R = 150^\circ$ and $\angle P + 3\angle Q = 170^\circ$, then $\angle P$ is equal to :
- PQR is a triangle. The bisectors of the internal angle $\angle Q$ and external angle $\angle R$ intersect at M. If $\angle QMR = 40^\circ$, then $\angle P$ is :
- Sachin sees one-fourth of his body (height) when he stands in front of a vertical mirror at a distance of 20 cm from it. How much of his body will he see if he steps back and stands 40 cm from the mirror?
Need Expert Advice?
