Polygon Angle Properties
An 8-sided polygon is called an octagon. The sum of the interior angles of an n-sided polygon is given by the formula:
$ \text{Sum of Interior Angles} = (n-2) \times 180^\circ $
For an 8-sided polygon ($n=8$), the total sum of its interior angles is:
$ (8-2) \times 180^\circ = 6 \times 180^\circ = 1080^\circ $
Calculating the 8th Interior Angle
We are given that the sum of 7 interior angles is $1000^\circ$. To find the measure of the 8th interior angle, we subtract this sum from the total sum of interior angles:
$ \text{8th Interior Angle} = (\text{Total Sum}) - (\text{Sum of 7 Angles}) $
$ \text{8th Interior Angle} = 1080^\circ - 1000^\circ = 80^\circ $
Exterior Angle Calculation
For any polygon, the sum of an interior angle and its corresponding exterior angle is $180^\circ$.
$ \text{Interior Angle} + \text{Exterior Angle} = 180^\circ $
To find the 8th exterior angle, we use the calculated 8th interior angle:
$ \text{8th Exterior Angle} = 180^\circ - \text{8th Interior Angle} $
$ \text{8th Exterior Angle} = 180^\circ - 80^\circ = 100^\circ $
Similar Questions
- The number of triangles formed by diagonals from one vertex of an octagon is:
- The sum of all interior angles of a 20-sided polygon is:
- If the measure of an exterior angle of a regular polygon is $20^\circ$, determine the total number of its sides.
- What is the minimum distance between centers of two circles having radii 5 cm and 3 cm such that exactly three common tangents exist?
- In a circle, angle subtended by chord AB at the center is $80^\circ$. What is the measure of angle $\angle ACB$, where C lies on the circle?
- In a circle with center O, two chords, AB and CD, cross each other at right angles. if the distance from the center O to chord AB is 3 cm, while the distance from O to chord CD is 4 cm. What is the radius of the circle?
- If the angle subtended by a chord at the center is $150^\circ$, what is the angle subtended at a point on the circle in the same segment?
- A triangle ABC has a circle inscribed within it with sides a, b, c. The area of the triangle is A. What is the radius of the inscribed circle?
- In a triangle ABC, if the angle bisectors of $\angle B$ and $\angle C$ intersect at point I, and $\angle BIC = 110^\circ$, what is the measure of $\angle A$?
- In triangle PQR, ST is parallel to QR. If PS=5cm, SQ=10cm, and PT=6cm, find TR.
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.
