Question

2. In the figure, what is the value of x?

Answer 1

Answer:

40°

Step-by-step explanation:

As per the provided information in the given question, we have :

• ∠AOC = 60°
• ∠BOC = 3x
• AB is a straight line.

We've been asked to calculate the measure of ∠BOC.

Here, ∠AOC and ∠BOC are making linear pair of angles.

$\odot$ Linear pair : Linear pair of angles are nothing but the two adjacent angles of which non-common arms are two opposite rays. Now, as these both angles are making linear pair so,

$\longrightarrow \sf{\quad { \angle AOC + \angle BOC = 180^\circ }}$

Substitute the measure of ∠AOC and the expression of ∠BOC.

$\longrightarrow \sf{\quad { 60^\circ+ 3x = 180^\circ }}$

Transposing the like terms.

$\longrightarrow \sf{\quad {3x= 180^\circ -60^\circ }}$

Performing subtraction of the terms in RHS.

$\longrightarrow \sf{\quad {3x= 120^\circ }}$

Now, transpose 3 from LHS to RHS, its arithmetic operator will get changed.

$\longrightarrow \sf{\quad {x= \cancel{\dfrac{120^\circ}{3}} }}$

Dividing 120° by 3.

$\longrightarrow \quad\underline {\boxed{ \textbf{\textsf{ x= 40}}^\circ }}$

∴ The value of x is 40°.

$\underline{ \qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}$

Learn More :

○ Measure of straight angle = 180°

○ If a ray stands on a line then the sum of the adjacent angles so formed is 180°.

○ The sum of the angles of a linear pair is 180°.

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