The ratio between an exterior angle and the interior angle of a regula

1.	The ratio between an exterior angle and the interior angle of a regular polygon is1:5. Find(i) the measure of each exterior angle (ii) the measure of each interior angle(iii) the number of sides in the polygon
Answer» Answer: Step-by-step explanation: Let the EXTERIOR angle be X and INTERIOR angle be 5x Therefore, 5x + x=180° [linear pair] ⇒ x=[180/6]° ⇒x =30° (i) Measure of the exterior angle is x=30° (ii) measure of each interior angle is 5x=5 x 30°=150° (iii) 360°/x where x is the measure of each exterior angle , gives US the no.of sides Therefore, 360° ÷ 30°=12 12 sides Please mark it the brainliest.

The ratio between an exterior angle and the interior angle of a regular polygon is1:5. Find(i) the measure of each exterior angle (ii) the measure of each interior angle(iii) the number of sides in the polygon

Answer»

Answer:

Step-by-step explanation: Let the EXTERIOR angle be X and INTERIOR angle be 5x

Therefore,

5x + x=180° [linear pair]

⇒ x=[180/6]°

⇒x =30°

(i) Measure of the exterior angle is x=30°

(ii) measure of each interior angle is 5x=5 x 30°=150°

(iii) 360°/x where x is the measure of each exterior angle , gives US the no.of sides

Therefore,

360° ÷ 30°=12

12 sides

Please mark it the brainliest.