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प्रश्न
Three of the exterior angles of a hexagon are 40°, 51 ° and 86°. If each of the remaining exterior angles is x°, find the value of x.
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उत्तर
The sum of all exterior angles of any polygon is always: 360∘
The total of the six exterior angles is: 40∘ + 51∘ + 86∘ + x + x + x = 360∘
Simplify: 177∘ + 3x = 360∘
Subtract 177∘ from both sides: 3x = 183∘
Divide by 3: `x=(183°)/3 = 61°`
Each of the remaining three exterior angles is: 61∘
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संबंधित प्रश्न
Fill in the blanks :
In case 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°____ |
Find the number of sides in a regular polygon, if its interior angle is: 135°
Find the number of sides in a regular polygon, if its exterior angle is: two-fifth of right angle
Is it possible to have a regular polygon whose interior angle is : 170°
Is it possible to have a regular polygon whose each exterior angle is: 40° of a right angle.
The exterior angle of a regular polygon is one-third of its interior angle. Find the number of sides in the polygon.
The ratio between the exterior angle and the interior angle of a regular polygon is 1 : 4. Find the number of sides in the polygon.
AB, BC and CD are three consecutive sides of a regular polygon. If angle BAC = 20° ; find :
(i) its each interior angle,
(ii) its each exterior angle
(iii) the number of sides in the polygon.
The ratio between the number of sides of two regular polygons is 3 : 4 and the ratio between the sum of their interior angles is 2 : 3. Find the number of sides in each polygon.
The sum of interior angles of a regular polygon is thrice the sum of its exterior angles. Find the number of sides in the polygon.
