Question: Find the value of 'x' in Fig.1, if: i) y= 3/2x, ii) y=111°.
The line AB is a straight line, hence the angle AOB = 180º
hence the sum of the angles comprising the angle AOB = 180º
i.e. x + y/2 + x = 180º
1) y = (3/2)x
so, x + (3/2)x + x/2 = 180
x + 2x 180
3x = 180
x = 60º
2) y = 111º
so, x + 111 + x/2 = 180
x + x/2 = 180 - 111 = 69
3x/2 = 69
x/2 = 23
x = 46º