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Find the angle which measures twice its supplement.
A) 100
B) 110
C) 120
D) 130
Answer
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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.
Complete step-by-step answer:
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.
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.
Complete step-by-step answer:
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.
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