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Lines and Angles — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsLines and Angles1 Mark
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.

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