Answer
Verified
397.2k+ views
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.
Recently Updated Pages
The branch of science which deals with nature and natural class 10 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Define absolute refractive index of a medium
Find out what do the algal bloom and redtides sign class 10 biology CBSE
Prove that the function fleft x right xn is continuous class 12 maths CBSE
Find the values of other five trigonometric functions class 10 maths CBSE
Trending doubts
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Summary of the poem Where the Mind is Without Fear class 8 english CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Write an application to the principal requesting five class 10 english CBSE
What organs are located on the left side of your body class 11 biology CBSE
What is the z value for a 90 95 and 99 percent confidence class 11 maths CBSE