Question

Determine which statement is true. A) t || u and v || w B) t || w and u || v C) t || v and u || w D) t || u and u || v

Answer 1

Answer:

the answer is c

Answer 2

Answer:

Option C) is correct

Step-by-step explanation:

Consider the attached figure:

As $\angle 1$ and $120^{\circ}$ form a linear pair,

$\angle 1+120^{\circ}=180^{\circ}\\\angle 1=180^{\circ}-120^{\circ}\\=60^{\circ}$

$\angle 1=\angle 2=60^{\circ}$ and $\angle 1 , \angle 2$ form a pair of corresponding angles, so $t||v$

( we know that if corresponding angles are equal , lines are parallel )

Also, as $\angle 3\,,\,110^{\circ}$ form a linear pair, so

$110^{\circ}+\angle 3=180^{\circ}\\\angle 3=180^{\circ}-110^{\circ}\\=70^{\circ}$

Now as $\angle 3=\angle 4=70^{\circ}$ and $\angle 3\,,\,\angle 4$ form a pair of alternate interior angles, so $u||w$

So, option C) is correct