Consider the following statement: When two straight lines interse…

MCQ

Consider the following statement: When two straight lines intersect:
$i.$ Adjacent angles are complementary
$ii.$ Adjacent angles are supplementary
$iii.$ Opposite angles are equal
$iv.$ Opposite angles are supplementary
Of these statements

A
$(i)$ and $(ii)$ are correct
✓
$(ii)$ and $(iii)$ are correct
C
$(i)$ and $(iv)$ are correct
D
$(ii)$ and $(iv)$ are correct

✓

Answer

Correct option: B.

$(ii)$ and $(iii)$ are correct

Let two lines $AB$ and $CD$ intersect each other at $O$.
Now,
We can see from fogure any two adjacent angles
$\angle\text{AOD}$ and $\angle\text{DOB},\angle\text{DOB}$ and $\angle\text{BOC}$ etc are supplementary because their sum is $180^\circ$.
$\angle\text{AOD}+\angle\text{DOB}=180^\circ$
$\angle\text{DOB}+\angle\text{BOC}=180^\circ$
So two adjacent angles are always supplementary.
Now,
Two opposite angle like $\angle\text{AOC}$ and $\angle\text{DOB},\angle\text{AOD}$ and $\angle\text{COB}$ are always equal to each other as they are vertically opposite angles
$\angle\text{AOC}=\angle\text{DOB}$
$\angle\text{AOD}=\angle\text{COB}$
Hence statement $(ii)$ and $(iii)$ are correct.