Question

Calculate $\angle AOC,\angle BOD$ and $\angle AOE$ in the adjacent figure given that $\angle COD={90}^o,\angle BOE={72}^o$ and AOB is a straight line.

Answer 1

Since AOB is a straight line, we have

$\angle AOE+\angle BOE={180}^o$

$=3x^o+{72}^o={180}^o$

$\Rightarrow 3x^o={108}^o\Rightarrow x={36}^o$

We also know that

$\therefore \angle AOC+\angle COD+\angle BOD={180}^o$ ($\because$ straight angle)

$\Rightarrow x^o+{90}^o+y^o={180}^o$

$\Rightarrow {36}^o+{90}^o+y^o={180}^o$

$y^o={180}^o-{126}^o={54}^o$

$\therefore \angle AOC={36}^o,\angle BOD={54}^o$ and $\angle AOE={108}^o$