Question

two complementry angles are such that the smaller angle is 10 degree more then the 3/5 times of greater find these angles

Answer 1

SOLUTION :

Let or Suppose the greater angle be 'x'.
Let the smaller angle be 'y'.

Complementary angles at the angles whose addition or sum is equal to 90 degree .

Hence ,
x + y = 90 ...................(1)

Now by given condition ,
y + 10 = 3/5 * x
y = 3/5x - 10
by taking L.C.M
y = 3/5x - 10/1 * 5
y = 3/5x - 50/5
y = 3x - 50/5 .............(2)

Subsitute equation (2) in (1)

x + 3x - 50/5 = 90
by taking L.C.M.
5x + 3x - 50/5 = 90
8x - 50 = 90 * 5
8x - 50 = 450
8x = 450+50
8x = 500
x = 500/8
x = 62.5

therefore the greater angle is 62.5 degree

therefore measure of smaller angle is ,
x + y = 90
62.5 + y = 90
y = 90 - 62.5
y = 27.5

Therefore measure of greater angle and smaller angle is 62.5 degree and 27.5 degree .