Question

# Find the angle which measures twice its supplement.A) 100B) 110C) 120D) 130

Hint: The two angles whose sum is equal to ${180^ \circ }$ are supplement angles of each other i.e.
If $\angle a + \angle b = {180^ \circ }$ then $\angle a$ and $\angle b$ are supplements of each other.
Here we will assume one angle to be x and another angle to be 2x and then solve for the value of x.

Let us assume the first angle to be x and the other angle to be 2x.
Now we know that the sum of supplementary angles is ${180^ \circ }$
Therefore, we will add these angles and put it equal to ${180^ \circ }$
$x + 2x = {180^ \circ }$
Solving for the value of x we get:-
$3x = {180^ \circ }$
Dividing the equation by 3 we get:-
$x = \dfrac{{{{180}^ \circ }}}{3} \\ x = {60^ \circ } \\$
Hence one angle is ${60^ \circ }$
Now since second angle is twice the first angle
Therefore multiplying the above value by 2 we get:
$2x = {60^ \circ } \times 2 \\ 2x = {120^ \circ } \\$
Now since we had to find the measure of the angle which is twice its supplement.
Hence we will consider the angle ${120^ \circ }$

So, the correct answer is “Option C”.

Note: Students should keep in mind that two supplementary angles take place by 180 degree.
Also, three or more angles also may sum to 180°, but they are not considered supplementary.