Question

When two complementary angles $\angle AOB\&\angle BOC$ are adjacent to each other, which of the following is correct?

• A. $\angle AOC={180}^o$
• B. $\angle AOC={90}^o$
• C. $\angle AOB={90}^o$
• D. None of the above.

Answer 1

The correct option is B $\angle AOC={90}^o$

When measures of two complementary angles are added, it results in ${90}^o.$
$\therefore \angle AOB+\angle BOC={90}^o$

Given that these two angles $\angle AOB\&\angle BOC$ are kept adjacent to each other that means both angles share common ray $OB$.

Hence, $\angle AOC={90}^o$
A perpendicular ray $OA$ makes ${90}^o$ with its base $OC$.

$\therefore$ When two complementary angles are adjacent to each other, they represent a perpendicular line with the base.