Question

In a pair of supplementary angles, the greater angle exceeds the smaller by 50°. Express the given situation as a system of linear equations in two variables and hence obtain the measure of each angle.

Answer 1

Let x and y be supplementary angles, x > у.

∴ x + y = 180°  ...(i)

According to question,

x = y + 50

x − y = 50  .....(ii)

By adding equations (i) and (ii),

2x = 230°

x = `(230°)/2`

x = 115°

Put the value of x in the equation (i).

x + y = 180°

115° + y = 180°

y = 180° − 115°

y = 65°

Hence, the required angles are 115° and 65°.