Question

Form the pair of linear equations for the following problem and find their solution by substitution method.

The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them.

Answer 1

Let the larger of the two supplementary angles be x.

And the smaller angle is y.

Hence case (II)

x - y = 18°            ...(i)

x + y = 180°         ...(ii)

(The sum of supplementary angles is 180°.)

Now from equation (i)

x - y = 18°

⇒ x = 18° + y

Now on putting the value of x in equation (ii)

x + y = 180°

⇒ 18° + y + y = 180°

⇒ 18° + 2y = 180°

⇒ 2y = 180° – 18°

⇒ 2y = 162°

⇒ y = ${\displaystyle \frac{{162}^{\circ }}{2}}$

⇒ y = 81°

Putting the value of y in equation (i)

⇒ x = 18° + y

⇒ x = 18° + 81°

⇒ x = 99°

Hence, the larger angle is 99° and the smaller angle is 81°.