Question

Find the angle $\angle HGE$ for the given figure using corresponding angles and alternate interior angles. Given $\angle DAB={105}^o.$
Here $AB\parallel DE\parallel HG\&AD\parallel BH\parallel GE$

• A. ${15}^o$
• B. ${105}^o$
• C. None of the above.
• D. Insufficient data.

Answer 1

The correct option is B ${105}^o$

Let's extend the parallel lines in the given figure.

For the parallel lines $DA$ and $HB{B}^{/},$ $\angle 1$ and $\angle 2$ are alternate interior angles.
Hence, $\angle 1=\angle 2$

For the parallel lines $AB$ and $H^{/}G,$ $\angle 2$ and $\angle 3$ are corresponding angles.
$\therefore \angle 2=\angle 3$

Finally, for the parallel lines $HC$ and $GE,$ $\angle 3$ and $\angle 4$ are corresponding angles.
Hence, $\angle 3=\angle 4$

$\therefore \angle 4=\angle 3=\angle 2=\angle 1={105}^o$