Mathematics

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.

2 Likes

Let x be the larger angle and y be the smaller angle.

Given,

Angles are supplementary.

∴ x + y = 180° ………..(1)

Given,

Larger of two supplementary angles exceeds the smaller by 18 degrees.

∴ x - y = 18° ………….(2)

Solving equation (2),

⇒ x - y = 18°

⇒ x = 18° + y ………..(3)

Substituting value of x from equation (3) in equation (1), we get :

⇒ 18° + y + y = 180°

⇒ 2y = 180° - 18°

⇒ 2y = 162°

⇒ y = $\dfrac{162°}{2}$ = 81°.

Substituting above value of y in equation (3), we get :

⇒ x = 18° + 81° = 99°.

Hence, pair of linear equations are x + y = 180° and x - y = 18°, where x and y are two angles such that x > y; x = 99° and y = 81°.

Answered By

2 Likes