Question

From the following figure, find the value of $\angle$ AOD and $\angle$ BOD.

• A. $\angle$ AOD = 138° and $\angle$ BOD = 42°
• B. $\angle$ AOD = 42° and $\angle$ BOD = 138°
• C. $\angle$ AOD = 120° and $\angle$ BOD = 60°
• D. $\angle$ AOD = 130° and $\angle$ BOD = 50°

Answer 1

The correct option is A $\angle$ AOD = 138° and $\angle$ BOD = 42°


Given, $\angle$ COA = 42°.

$\angle$ AOD + $\angle$ COA = 180° (Linear Pair)
$\angle$ AOD + 42° = 180°
$\angle$ AOD = 180° - 42° = 138°
Hence, $\angle$AOD = 138°.

$\angle$ COA = $\angle$ BOD = 42° (Vertically Opposite angles)

Thus, $\angle$ AOD = 138° and $\angle$ BOD = 42°.