Find the radian measure of the interior angle of a regular:
(i) Pentagon
(ii) Hexagon
(iii) Octagon
Answers
Answer:
108°
120°
135 °
Step-by-step explanation:
Find the radian measure of the interior angle of a regular:
(i) Pentagon
(ii) Hexagon
(iii) Octagon
Sum of internal angle of polygon = (n-2) * 180°
Interior Angle = (n-2) * 180° / n
Interior angle of Pentagon = (5-2) * 180° / 5 = 3 * 180° / 5 = 108°
Interior angle of Hexagon = (6-2) * 180° / 6 = 4 * 180° / 6 = 120°
Interior angle of Octagon = (8-2) * 180° / 8 = 6 * 180° / 8 = 135 °
Answer:
3π/5
2π/3
3π/4
Step-by-step explanation:
Find the radian measure of the interior angle of a regular:
Formula to use
Interior Angle = (n-2) * 180° / n
Conversion
180° = π
1° = π/180°
(i) Pentagon
Interior angle of Pentagon = (5-2) * 180° / 5 = 3 * 180° / 5 = 108°
108° = π(108)/180° = 3π/5
(ii) Hexagon
Interior angle of Hexagon = (6-2) * 180° / 6 = 4 * 180° / 6 = 120°
120° = π(120)/180° = 2π/3
(iii) Octagon
Interior angle of Octagon = (8-2) * 180° / 8 = 6 * 180° / 8 = 135
135° = π(132)/180° = 3π/4