Question

In the diagram, $\overrightarrow{OB}$bisects $\angle AOC$and $\overleftrightarrow{EC}\perp \overleftrightarrow{OD}$.

Find the value of x.

$m\angle 1=2x$, $m\angle 2=6x+2$.

Short answer

The value of xis 11.

Step-by-step solution

Step 1. Observe the given diagram.

The given diagram is:

Step 2. Write the relation between the angles ∠1 and ∠2.

As, $\overleftrightarrow{EC}\perp \overleftrightarrow{OD}$, therefore the lines EC and OD are perpendicular lines.

Therefore, by using the definition of perpendicular lines it can be said that the measures of the angle $\angle DOE$is $90°$.

That implies, $m\angle DOE=90°$.

Now, by using the angle addition postulate it can be said that $m\angle DOE=m\angle 1+m\angle 2$.

Therefore, the relation between the angles ∠1 and ∠2 is:

$m\angle DOE=m\angle 1+m\angle 2$

$90=m\angle 1+m\angle 2$

Step 3. Find the value of x.

As, $m\angle 1+m\angle 2=90°$, $m\angle 1=2x$and $m\angle 2=6x+2$.

Therefore, the value of x is given by:

role="math" localid="1646589364482" $m\angle 1+m\angle 2=90°$

$2x+6x+2=90°$

$8x+2=90°$

$8x=90°-2$

$8x=88°$

$x=\frac{88}{8}$

$x=11$

Therefore, the value of x is 11.