Question

Find the degree and radian measure of exterior and interior angle​

Answer 1

Answer:

Step-by-step explanation:

Interior angle of polygon: 180°(n - 2) / n = α

Exterior angle of polygon: 180° - α

Radians = (degrees)×π/180

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(i). Pentagon (5 sides):

Interior angle: [180°(5 - 2)] / 5 = 108° =  3π/5 (radians);

Exterior angle: 180° - 108° = 72° = 2π/5 (radians);

(ii). Hexagon (6 sides):

Interior angle: 180°(6 - 2) / 6 = 120° = 2π/3 (radians);

Exterior angle: 180° - 120° = 60° = π/3 (radians);

(iii). Septagon/heptagon (7 sides):

Interior angle: 180°(7 - 2) / 7 = 128.57° ≈ 7π/10 (radians);  

Exterior angle: 180° - 128.57° = 51.43° ≈ 3π/10 (radians);

(iv). Octagon (8 sides):

Interior angle: 180°(8 - 2) / 8 = 135° = 3π/4 (radians);

Exterior angle: 180° - 135° = 45° = π/4 (radians).

Answer 2

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 .