Question

Three angles of a quadrilateral are in the ratio 2:3:7. The mean of these angles is 64 degrees .Find all the four angles.

Answer 1

let those three angles be 2x, 3x, and 7x
let the fourth angle be y
So as we know sum of all angles in quadrilateral should be 360
So
2x + 3x + 7x + y = 360
y + 12x = 360
y = 360 - 12x........(1)

"the mean of these angles is 64"
I will assume you mean the mean of the 3 angles.
(2x+3x+7x)/3 = 64
12x/3=64
4x = 64
x = 16.......(2)
From.equation 1 and 2
then y = 360-192 = 168
Answer is
the 4 angles are : 32° , 48°, 112°, and 168