Question

If AB||CD||FG and BC||FE in the given figure, then the measure of reflex $\angle DEF$ is

• A. ${200}^0$
• B. ${275}^0$
• C. ${280}^0$
• D. ${180}^0$

Answer 1

The correct option is C ${280}^0$

Constrution: Produce BC upto point X.
Draw a line WZ through E and parallel to CD. WZ intersects BX at Y.





$AB||CD$ ...........(1)
$CD||YE$...........(2) [Construction]
From (1) and (2), we get
$AB||YE$
Since $AB||YE$ and $BY$ is transversal,
$\therefore \angle a={55}^0$
Because of alternate interior angles



$BY||FE[\therefore BC||FE]$
$\angle a=\angle b$ [Corresponding angles are equal]
$\Rightarrow \angle b={55}^0$
Since $CD||YE$ and $DE$ is a transversal
135 degrees + < C = 180 degrees
< C = 45 degrees
Since WEZ is a line,
$\therefore \angle b+\angle c+\angle DEF={180}^0$
$\Rightarrow {55}^0+{45}^0+\angle DEF={180}^0$
$\Rightarrow {100}^0+\angle DEF={180}^0$
$\Rightarrow \angle DEF={80}^0$
Now $\angle DEF+Reflex\angle DEF={360}^0$
$\Rightarrow {80}^0+Reflex\angle DEF={360}^0$
$\Rightarrow Reflex\angle DEF={280}^0$