Question

The angle which is twice its supplement is-
$A.\;{120^o}$
$B.\;{90^o}$
$C.\;{60^o}$
$D.\;{30^o}$

Answer 1

Hint: A general knowledge of angles and linear equations is required. The supplement of a given angle is the angle which makes a sum of ${180^o}$, that is a linear angle, with the given angle. So, first we will assume the angle using a variable x, and then form the equation that x is twice its supplement, that is $({180^o} - x)$. We will then solve the equation to find the value of x.

Complete step-by-step answer:
We need to find an angle which is twice its supplement. So, let us assume the angle to be x. The supplement of a given angle is such that it makes a sum of ${180^o}$ with the original angle. So, let the supplement be y. We can write that-
$x + y = {180^o}$
$y = {180^o} - x$...(1)
It has also be given that the given angle is twice its supplement, so we can write that-
$x = 2y$
Substituting the value of y from equation (1), we can write that-
$x = 2\left( {180 - x} \right)$
$x = 360 - 2x$
Transposing all the terms to LHS, we can write that-
$x + 2x - 360 = 0$
$3x - 360 = 0$
$3x = 360$
$x = \dfrac{{360}}{3} = {120^o}$
This is the required angle which is twice its supplement, $y = 180 - 120 = {60^o}$. The correct option is A.

Note: A major point of confusion here is between option A and C. Many students often mark option C as the answer, which is ${60^o}$. But this is incorrect, because we need to find the angle which is twice its supplement. When we look closely, ${60^o}$ is actually half of its supplement, and hence it is a wrong answer.