Question

Two angles measure ${(30 - a)^0}$ and ${(125 + 2a)^0}$ . If each one is the supplement of the other, then the value of a is:
A. ${45^0}$
B. ${35^0}$
C. ${25^0}$
D. ${65^0}$

Answer 1

Hint:This question is using the concept of supplementary angles. The pair of angles having sum total as ${180^0}$ , is termed as supplementary of each other. By applying this, we can get a linear equation in variable ‘a’. By solving the linear equation, we can get the value of a.

Complete step-by-step answer:
Let us suppose the first angle is,
$\alpha = 30 - a………. (1)$
And the second angle is,
$\beta = 125 + 2a………. (2)$
As, it is given in the question that these two angles $\alpha $ and $\beta $ are supplementary to each other.
Then we have,
$\alpha + \beta = 180$
So, by substituting the values in above equation from equations (1) and (2) , we get
$\alpha + \beta = 180$
$
   \Rightarrow (30 - a) + (125 + 2a) = 180 \\
   \Rightarrow a + 155 = 180$
The above equation is a linear equation in one variable.
We solve it to get value of ‘a’,
$a = 180-155$
$ \Rightarrow a = 25$
$\therefore $ The value of a is ${25^0}$ .

So, the correct answer is “Option C”.

Additional Information:(1) Supplementary angles are having sum total of ${180^0}$ and complementary angles are having sum total of ${90^0}$.
(2) The expression of equality of two algebraic expressions involving one or more variables is known as equation. Also, an equation in which the highest power of the variable is one with one or more variables, is known as linear equation. For example, the algebraic equation ax + b = 0 is a linear equation in one variable. Similarly, the algebraic equation ax + by + c = 0, is a linear equation in two variables.

Note:This problem is a word problem of linear equations. First, we need to make the equation based on given terms in it. Then this linear equation in one variable has to be solved. Simple algebraic substitution and further simplification will solve such equations with required result.