The angle which makes a linear pair with an angle of \[61^\circ \] is of
A. \[29^\circ \]
B. \[61^\circ \]
C. \[122^\circ \]
D. \[119^\circ \]

Question

The angle which makes a linear pair with an angle of $$61^\circ $$ is ofA. $$29^\circ $$B. $$61^\circ $$C. $$122^\circ $$D. $$119^\circ $$

Vedantu Content Team · Accepted Answer

Hint: In this problem first of all we will draw a rough diagram. We will approach this problem by using the definition of a linear pair of angles i.e., Linear pair of angles are formed when two lines intersect each other at a single point. In this problem, we have given one of the angles as $$61^\circ $$ so we will let the other angle as $$x$$ . Then we will use one of the properties of a linear pair of angles, that is the sum of angles of a linear always equal to $$180^\circ $$ . After that we will substitute the values in the above conditions and simplify. Hence, we will get our required result. Complete step by step answer: Here, we have to find an angle which makes a linear pair with an angle of $$61^\circ $$.Let the angle be $$x$$. Now we know that two angles are said to be a linear pair if they are adjacent. So, let’s draw a rough diagram,\n    \n    \n    \n    \n  Now as we know, the sum of angles of a linear is always equal to $$180^\circ $$. Therefore, from the diagram,$$\angle DCA + \angle DCB = 180^\circ $$On substituting the values, we get$$ \Rightarrow x + 61^\circ  = 180^\circ $$$$ \Rightarrow x = 180^\circ  - 61^\circ $$On subtracting, we get$$ \therefore x = 119^\circ $$Hence, the angle which makes a linear pair with an angle of $$61^\circ $$ is of $$119^\circ $$.So, the correct answer is option D.Note: As we know that the sum of angles of linear pair is always $$180^\circ $$.$$ \Rightarrow \angle DCA + \angle DCB = 119^\circ  + 61^\circ  = 180^\circ $$In this way, we can check whether the solution is correct or wrong. Also sometimes many students get confused between adjacent angles and linear pairs. Adjacent angles are those that have a common vertex and common side but do not overlap while linear pairs are those that are adjacent, and the measure is $$180^\circ $$ . So, don’t get confused between the two.Example of Linear Pair,\n    \n    \n    \n    \n  Example of Adjacent angle\n    \n    \n    \n    \n

The angle which makes a linear pair with an angle of \[61^\circ \] is ofA. \[29^\circ \]B. \[61^\circ \]C. \[122^\circ \]D. \[119^\circ \]

The angle which makes a linear pair with an angle of \[61^\circ \] is of
A. \[29^\circ \]
B. \[61^\circ \]
C. \[122^\circ \]
D. \[119^\circ \]