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°.
Important Questions from Geometry (Notes)
- 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 :
- A $2\text{ m}$ long ladder is to reach a wall of height $1.75\text{ m}$. The largest possible horizontal distance of the ladder from the wall could be
Three-quarters of a circle is shown in the figure; OA and OB are two radii perpendicular to each other. C is a point on the circle.
What is angle ACB?
