Question

Look at the following figure and fill in the blanks :

If $\angle AOB=45°$, then $\angle DOE=$……………….

Answer 1

Linear Pair :

A linear pair can be defined as two adjacent angles that add up to $180°$ or two angles that form a line or a straight angle when combined together. As given in the figure :

So, $\angle 1$ and $\angle 2$ form a linear pair.

Similarly, as per the question :

$\angle AOB,\angle AOE$ and $\angle DOE$ form a linear pair.

So, $\angle AOB+\angle AOE+\angle DOE=180°$

$\Rightarrow 45°+40°+\angle DOE=180°$ ($\because$it is given as $\angle AOB=45°$ and $\angle AOE=40°$ )

$\Rightarrow \angle DOE+85°=180°$

$\Rightarrow \angle DOE=180°-85°$ (By transposing $85°$from L.H.S. to R.H.S.)

$\Rightarrow \angle DOE=95°$

Hence the required value of $\angle DOE$ is $95°$, i.e. $\angle DOE=95°$.