Question

solve these questions

Answer 1

1)let the first angle be x

then the angles are - x,x+10,x+20,x+40

we know
x + x+10 + x+20 + x+30= 360
4x + 60 = 360
x + 15 = 90
x = 75

therefore the angles are -
75 , 85, 95 , 105

Answer 2

Let one angle be 'a'

Other angles will be a + 10, a + 20 and a + 30

Now sum of all angles of a quadrilateral is 360°
So,
a + a + 10 + a + 20 + a + 30 = 360
4a + 60 = 360
4a = 300
a = 75

The angles are 75°, 85°, 95°, 105°

Let 4 numbers be in AP such that
a - 3d, a - d, a + d, a + 3d

a - 3d + a - d + a + d + a + 3d = 32
4a = 32
a = 8

Now we have find the product of extremes and product of means

Product of extremes = (a - 3d)(a +3d) =
(8 - 3d)(8 + 3d) = 64 - 9d^2

Product of means = (a - d)(a + d) = a^2 - d^2

64 - 9d^2/a^2 - d^2 = 7/15

960 - 135d^2 = 448 - 7d^2
- 135d^2 + 7d^2 = 448 - 960
-128d^2 = -512
d^2 = 512/128
d^2 = 4
d = 2

The numbers are -
a - 3d = 8 - 3 x 2 = 2
a - d = 8 - 2 = 6
a + d = 8 + 2 = 10
a + 3d = 8 + 3 x 2 = 14
Required numbers are 2,6,10,14


Hope This Helps You!