Question

One of the supplementary angles exceeds the other by 120°. Express the given information as a system of linear equations in two variables. Hence, find the measure of both the angles.

Answer 1

Let, two angles be x and y

So, x + y = 180°   ...(i) [∵ For supplementary angle]

Also x – y = 120°   ...(ii) [By given conditions]

From (i) and (ii), we get

x + y = 180° 
x – y = 120°
+   +    +       
    2x = 300°

`x = 300^circ/2`

∴ x = 150°

Now, put x = 150° in (i), we get

150° + y = 180°

y = 180° – 150°

∴ y = 30°

So, x = 150° and y = 30°.