Question

Form the pair of linear equations for the following problems and find their solution by substitution method.
The larger of two supplementary angles exceeds the smaller by $18 ^\circ $. Find them.

Answer 1

Hint: 2 angles are supplementary when they add up to $180 ^\circ $. They don't have to be next to each other, just so long as the total is $180 ^\circ $.
The substitution method functions by substituting the one value with the other in a linear equation.

Complete step-by-step answer:
We have to find the values of the 2 angles. Given that they are supplementary and the larger angle exceeds the smaller by $180 ^\circ $.
Therefore let the larger angle be x and smaller angle be y.
Condition of supplement angles, x+y=180
Larger angle exceeds smaller by 18 degrees, x=y+18
Now we substitute this value of x in the above condition
Therefore, x+y=180
y+18+y=180
2y+18=180
Subtracting 18 from both sides
2y=162
Dividing by 2 on both sides
y=81
Substituting this value on the any of the 2 linear equations
x=y+18
x=81+18
Therefore, x=99
Therefore the required 2 supplementary angles are $99 ^\circ $ and $81 ^\circ $.

Note: Students must be able to define different types of angles involved in simple geometric problems.
The word substitution method itself gives the clue that a linear variable must be substituted in order to get the correct answer.