Question

In the given figure below, points A, O, and C lie on the same line.
What is the sum of the measures of angle AOD and angle DOC?

• A. 90${}^o$
• B. 180${}^o$
• C. 270${}^o$
• D. 360${}^o$

Answer 1

The correct option is B 180${}^o$

$\Rightarrow$ In given figure points $A,O$ and $C$ lie on the same line, so they are collinear.

$\Rightarrow$ A linear pair is a pair of adjacent angles formed when two lines intersect and addition of angle form a straight line.

$\therefore$ $\angle AOD$ and $\angle DOC$ are linear pair.

$\Rightarrow$ The measure of a straight angle is ${180}^o$, so a linear pair of angles must add up to ${180}^o$.

$\therefore$ $\angle AOD+\angle DOC={180}^o.$