Questions & Answers

Question

Answers

A) 100

B) 110

C) 120

D) 130

Answer
Verified

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 \[{120^ \circ }\]

Also, three or more angles also may sum to 180°, but they are not considered supplementary.