Question

A ray OC is constructed on the line segment AB such that ∠BOC is x${}^{\circ }$. ∠AOC is

• A. x${}^{\circ }$
• B. 90 - x${}^{\circ }$
• C. 180 - x${}^{\circ }$
• D. 360 - x${}^{\circ }$

Answer 1

The correct option is C 180 - x${}^{\circ }$

AB is a straight line and the ray OC is drawn on the line segment AB.

Therefore,
$\angle$AOC + $\angle$BOC = 180${}^{\circ }$ ($\angle$AOC and $\angle$BOC are linear pair of angles)

$\angle$AOC = 180${}^{\circ }$ - $\angle$BOC

= 180${}^{\circ }$ – x${}^{\circ }$