Find the degree and radian measure of
exterior and interior angle of a regular
i) Pentagon ii) Hexagon
iii) Septagon iv) Octagon
Answers
Answer:
- Pentagon : exterior angle = 72° or 2π / 5 and interior angle= 108° or 3π / 5.
- Hexagon : exterior angle = 60° or π / 3 and interior angle= 120° or 2π/ 3.
- Septagon : exterior angle = (360° / 7) or 51.42° or 2π / 7 and interior angle= 900° / 7 or 128.57° or 5π / 7 .
- Octagon : exterior angle = 45° or π / 4 and interior angle= 135° or 3π / 4 .
Step-by-step explanation:
A regular polygon has all of the sides equal to each other and all the angles equal to each other.
Exterior Angle: these angles add up to 360°. Therefore, each exterior angle = (360° / n), where n is no. of sides of polygon.
Interior Angle: these angles add up to give 180°. Therefore, each interior angle = {(n-2)*180°}/n, where n is the no. of sides of polygon.
Also, Interior Angles = 180° - Exterior Angles
And, Radians = (π / 180°) * Degrees
Pentagon:
No. of sides, n = 5
∴ Degree measure of Exterior Angles = (360° / 5) = 72°
Radian measure = (π / 180°) * 72° = 2 π / 5
∴ Degree measure of Interior Angles = 180°- Exterior Angles= 180° - 72° = 108°
Radian measure = (π / 180°) * 108° = 3π / 5
Hexagon:
No. of sides, n = 6
∴ Degree measure of Exterior Angles = (360° / 6) = 60°
Radian measure = (π / 180°) * 60° = π / 3
∴ Degree measure of Interior Angles = 180° - Exterior Angles= 180° - 60° = 120°
Radian measure = (π / 180°) * 120° = 2π / 3
Septagon:
No. of sides, n = 7
∴ Degree measure of Exterior Angles = (360° / 7) or 51.42°
Radian measure = (π / 180°) * (360°/ 7) = 2π / 7
∴ Degree measure of Interior Angles = 180° - Exterior Angles= 180° - 360° / 7° = 900° / 7 or 128.57°
Radian measure = (π / 180°)*900°/7 = 5π / 7
Octagon:
No. of sides, n = 8
∴ Degree measure of Exterior Angles = (360° / 8) = 45°
Radian measure = (π / 180°) * 45° = π / 4
∴ Degree measure of Interior Angles = 180° - Exterior Angles= 180° - 45° = 135°
Radian measure = (π / 180°) * 135° = 3 π / 4
Answer:
I don't know
plz follow me!!!