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.
[tex]\odot [/tex] 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,
[tex] \longrightarrow \sf{\quad { \angle AOC + \angle BOC = 180^\circ }} \\ [/tex]
Substitute the measure of ∠AOC and the expression of ∠BOC.
[tex] \longrightarrow \sf{\quad { 60^\circ+ 3x = 180^\circ }} \\ [/tex]
Transposing the like terms.
[tex] \longrightarrow \sf{\quad {3x= 180^\circ -60^\circ }} \\ [/tex]
Performing subtraction of the terms in RHS.
[tex] \longrightarrow \sf{\quad {3x= 120^\circ }} \\ [/tex]
Now, transpose 3 from LHS to RHS, its arithmetic operator will get changed.
[tex] \longrightarrow \sf{\quad {x= \cancel{\dfrac{120^\circ}{3}} }} \\ [/tex]
Dividing 120° by 3.
[tex] \longrightarrow \quad\underline {\boxed{ \textbf{\textsf{ x= 40}}^\circ }} \\ [/tex]
∴ The value of x is 40°.
[tex] \underline{ \qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad} \\ [/tex]
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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