Question

If $DC\perp AB$, then $\angle$CDB is equal to

• A. 180${}^o$
• B. 45${}^o$
• C. 90${}^o$
• D. 120${}^o$

Answer 1

The correct option is C 90${}^o$

When two straight lines intersect at a point and form a linear pair of equal angles, they are perpendicular.

$\therefore$ $\angle CDB=\angle CDA$

A linear pair of angles is such that the sum of angles is ${180}^o.$

$\Rightarrow$ $\angle CDA+\angle CDB={180}^o$

$\Rightarrow$ $\angle CDB+\angle CDB={180}^o$

$\Rightarrow$ $2\angle CDB={180}^o$

$\therefore$ $\angle CDB={90}^o$.

Hence, $DC\perp AB,$ then, $\angle CDB={90}^o$