4. The ratio between an exterior angle and an interior angle of a regular polygon is 2 : 3. Find the number of sides in the polygon.
3. AB, BC and CD are the three consecutive sides of a regular polygon. If ∠BAC = 15o; find,
(i) Each interior angle of the polygon.
(ii) Each exterior angle of the polygon.
(iii) Number of sides of the polygon.
2. In a pentagon ABCDE, AB is parallel to DC and ∠A : ∠E : ∠D = 3 : 4 : 5. Find angle E.
1. Two angles of an eight-sided polygon are 142o and 176o. If the remaining angles are equal to each other; find the magnitude of each of the equal angles.
5. Three angles of a seven-sided polygon are 132o each and the remaining four angles are equal. Find the value of each equal angle.
4. In a polygon there are 5 right angles and the remaining angles are equal to 195o each. Find the number of sides in the polygon.
3. One angle of a six-sided polygon is 140o and the other angles are equal. Find the measure of each equal angle.
2. The angles of a pentagon are in the ratio 4 : 8 : 6 : 4 : 5. Find each angle of the pentagon.
1. The sum of the interior angles of a polygon is four times the sum of its exterior angles. Find the number of sides in the polygon.
Sum of Exterior Angles of any polygon is always 360 degrees.
And for n- sided polygon, the sum of the interior angle = (n-2) x 180 degrees
According to the problem sum of the interior angles is four times of the sum of the exterior angles,
therefore, (n-2) X 180 degrees = 4 x 360 degrees
let's simplify it,
(n-2) X 180 degrees = 1440 degrees
n-2 = 1440/180
n= 8+ 2
n= 10 polygon has 10 sides
4. The length, breadth and height of cuboid are in the ratio 6 : 5 : 3. If its total surface area is 504 cm2, find its volume.