In the figure, ∠AOC and ∠BOC form a linear pair. The value of x is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 30°
Two angles form a linear pair when they share an arm (here OC) and their other arms, OA and OB, lie on one straight line. Together they make a straight angle, so they add up to 180°.
The linear pair gives \(\angle AOC+\angle BOC=180^\circ\)
From the figure, \(\angle AOC=4x\) and \(\angle BOC=2x\), so \(4x+2x=180^\circ\)
That is \(6x=180^\circ\), so \(x=30^\circ\)