Question

In the figure, the value of $ a$ is:

• A. $20°$
• B. $15°$
• C. $5°$
• D. $10°$

Answer 1

The correct option is D

$10°$

Step 1: Calculate the value of $\angle AOB$

As we know, the angles on the same sides of a straight line formed on the same point are supplementary.

Now, since $CF$ is a straight line.

So, $\angle FOA+\angle AOB+\angle BOC=180°$

$\Rightarrow$ $90°+\angle AOB+40°=180°$

$\Rightarrow$ $\angle AOB+130°=180°$

$\Rightarrow$ $\angle AOB=180°-130°$

$\Rightarrow$ $\angle AOB=50°$

Step 2: Calculate the value of $a$

As we know, the vertically opposite angles formed by intersection of two straight lines are equal.

Then, since $AD$ and $BE$ are straight lines intersecting at point $O$.

So, $\angle DOE=\angle AOB$

$\Rightarrow$ $5a=\angle AOB$

$\Rightarrow$ $5a=50°$

$\Rightarrow$ $a=\frac{50°}{5}$

$\Rightarrow$ $a=10°$

Hence, $a=10°$, so option D is the correct option.