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 be the measure of the smaller angle and y be the measure of the greater angle.

The sum of two supplementary angles is always 180°.

x + y = 180°     ...(1)

The greater angle exceeds the smaller angle by 50°.     ...(Given)  

y = x + 50°     ...(2)

Substituting y = x + 50° into the (1) equation:

x + y = 180°

⇒ y + 50 + y = 180°

⇒ 2y = 180° − 50°

⇒ 2y = 130°

⇒ y = 65°

Now, substituting eqn. (2) 

x = y + 50°

⇒ x = 65° + 50°

⇒ x = 115°

∴ The smaller angle is 65° and the greater angle is 115°.