Fill in the blanks:
Incase of regular polygon, with:
no. of sides each exterior angle each interior angle
(i) ..8………… …………… ……………
(ii)..12….. …………… ……………
(iii) …………… ..72°………. ……………
(iv) …………… ..45°………. ……………
(v) …………… …………… ….150°…….
(vi) …………… …………… ….140°…….
Geometrical Shapes
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Question

Fill in the blanks:
Incase of regular polygon, with:
no. of sides each exterior angle each interior angle
(i) ..8………… …………… ……………
(ii)..12….. …………… ……………
(iii) …………… ..72°………. ……………
(iv) …………… ..45°………. ……………
(v) …………… …………… ….150°…….
(vi) …………… …………… ….140°…….

Geometrical Shapes

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KnowledgeBoat · Accepted Answer

(i) As per the properties of polygon, if there are n number of sides then each of its exterior angles is . n = 8 ⇒ = 45° Hence, each exterior angle = 45°. As per the properties of polygon, if there are n number of sides then each of its interior angles is . = = = = = 135° Hence, each interior angle = 135°. (ii) As per the properties of polygon, if there are n number of sides then each of its exterior angles is . n = 12 ⇒ = 30° Hence, each exterior angle = 30°. As per the properties of polygon, if there are n number of sides then each of its interior angles is . = = = = = 150° Hence, each interior angle = 150°. (iii) As per the properties of polygon, if there are n number of sides then each of its exterior angles is . Exterior angle = 72° ⇒ = 72° ⇒ n = ⇒ n = 5 Hence, number of sides = 5. As per the properties of polygon, if there are n number of sides then each of its interior angles is . n = 5 = = = = = 108° Hence, each interior angle = 108°. (iv) As per the properties of polygon, if there are n number of sides then each of its exterior angles is . Exterior angle = 45° ⇒ = 45° ⇒ n = ⇒ n = 8 Hence, number of sides = 8. As per the properties of polygon, if there are n number of sides then each of its interior angles is . n = 8 = = = = = 135° Hence, each interior angle = 135°. (v) As per the properties of polygon, if there are n number of sides then each of its interior angles is . ⇒ = 150° ⇒ (2n \- 4) x 90° = 150°n ⇒ 180°n \- 360° = 150°n ⇒ 180°n \- 150°n = 360° ⇒ 30°n = 360° ⇒ n = ⇒ n = 12 Hence, number of sides = 12. As per the properties of polygon, if there are n number of sides then each of its exterior angles is ⇒ = 30° Hence, each exterior angle = 30°. (vi) As per the properties of polygon, if there are n number of sides then each of its interior angles is . ⇒ = 140° ⇒ (2n \- 4) x 90° = 140°n ⇒ 180°n \- 360° = 140°n ⇒ 180°n \- 140°n = 360° ⇒ 40°n = 360° ⇒ n = ⇒ n = 9 Hence, number of sides = 9. As per the properties of polygon, if there are n number of sides then each of its exterior angles is . ⇒ = 40° Hence, each exterior angle = 40°. no. of sides| each exterior angle | each interior angle ------------|---------------------|-------------------- (i) 8 | 45° | 135° (ii) 12 | 30° | 150° (iii) 5 | 72° | 108° (iv) 8 | 45° | 135° (v) 12 | 30° | 150° (vi) 9 | 40° | 140°

Mathematics

Geometrical Shapes

Related Questions

The ratio between each interior angle of a regular polygon and each exterior angle of it is 3 : 2. The number of sides in the polygon is:
6
4
8
none of these

no. of sides	each exterior angle	each interior angle
(i) ..8…………	……………	……………
(ii)..12…..	……………	……………
(iii) ……………	..72°……….	……………
(iv) ……………	..45°……….	……………
(v) ……………	……………	….150°…….
(vi) ……………	……………	….140°…….

Mathematics

Geometrical Shapes

Related Questions

The ratio between each interior angle of a regular polygon and each exterior angle of it is 3 : 2. The number of sides in the polygon is:648none of these

The ratio between each interior angle of a regular polygon and each exterior angle of it is 3 : 2. The number of sides in the polygon is:
6
4
8
none of these