Question

In the following figure, if EO and FO are the angle bisectors and $\angle BEO$ = 40° and $\angle DFO$ = 50°. What can you conclude about the lines L and M?

• A. L is parallel to M.
• B. L is perpendicular to M.
• C. $\angle BEF+\angle DFE={100}^{\circ }+{80}^{\circ }={180}^{\circ }$
• D. L and M does not exist.

Answer 1

The correct option is A L is parallel to M.

Given, EO and FO are the angle bisectors and $\angle BEO$ = 40° and $\angle DFO$= 50°.

Then, $\angle FEO=\angle BEO$ = 40°.
$\angle EFO=\angle DFO$ = 50°.

We can write,
$\angle BEF=\angle BEO+\angle OEF$
$=40°+40°=80°$
$\angle DFE=\angle DFO+\angle OFE$
$=50°+50°=100°$
$\angle BEF+\angle DFE=100°+80°=180°.$

Hence, $\angle BEF$ and $\angle DFE$ form co- interior angles.
Then, L || M.