Question

In the given figure, $\overline{AB}$ is a straight line. Find the
value of $x$. Also find $\angle AOC,\angle COD$ and $\angle BOD$.

Answer 1

Since $\overline{AB}$ is a straight line, the sum of all the angles on $\overline{AB}$ at a point O is ${180}^o$.
∴$(3x+7{)}^o+(2x-19{)}^o+x={180}^o$
(𝐿𝑖𝑛𝑒𝑎𝑟 𝑎𝑛𝑔𝑙𝑒𝑠)
$⟹6x-12=180\Rightarrow 6x=192\Rightarrow x={32}^o$
$So,\angle AOC=(3x+7{)}^o=(3\times 32+7{)}^o={103}^o$,
$\angle COD=(2x-19{)}^o=(2\times 32-19{)}^o={45}^o,\angle BOD={32}^o$