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.
Let the measure of each equal angles are x.
Then we can write
3 × 132o + 4x = (2 × 7 – 4) 90o
4x = 900o – 396o
4x = 504o
x = 126o
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.
Let the number of sides of the polygon is n and there are k angles with measure 195o.
Therefore, we can write:
5 × 90o + k × 195o = (2n – 4) 90o
180on – 195o k = 450o – 360o
180on – 195ok = 90o
12n – 13k = 90o
In this linear equation n and k must be integer.
Therefore, to satisfy this equation the minimum value of k must be 6 to get n as integer.
Hence the number of sides are: 5 + 6 = 11.
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.
Let the angles of the pentagon are 4x, 8x, 6x, 4x and 5x.
Thus, we can write
4x + 8x + 6x + 4x + 5x = 540o
27x = 540o
x = 20o
Hence the angles of the pentagon are:
4×20o = 80o, 8×20o = 160o, 6×20o= 120o, 4×20o= 80o, 5×20o= 100o
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.
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.
3. The external dimensions of an open wooden box are 65 cm, 34 cm and 25 cm. If the box is made up of wood 2 cm thick, find the capacity of the box and the volume of wood used to make it.
2. The curved surface area and the volume of a toy, cylindrical in shape, are 132 cm2 and 462 cm3 respectively. Find, its diameter and its length.
1. The floor of a rectangular hall has a perimeter 250 m. If the cost of painting the four walls at the rate of ₹ 10 per m2 is ₹ 15,000, find the height of the hall.
4. The length of a hall is double its breadth. Its height is 3 m. The area of its four walls (including doors and windows) is 108 m2, find its volume.