Consider the following statement: When two straight lines intersect: 1. Adjacent angles are complementary 2. Adjacent angles are supplementary 3. Opposite angles are equal 4. Opposite angles are supplementary Of these statements

2. (ii) and (iii) are correct Solution: Let two lines AB and CD intersect each other at O. Now, We can see from fogure any two adjacent angles and , and etc are supplementary because their sum is 180°. + =180^ + =180^ So two adjacent angles are always supplementary. Now, Two opposite angle like and , and are always equal to each other as they are vertically opposite angles = = Hence statement (ii) and (iii) are correct.

Consider the following statement: When two straight lines interse…

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Question

Consider the following statement:
When two straight lines intersect:

Adjacent angles are complementary
Adjacent angles are supplementary
Opposite angles are equal
Opposite angles are supplementary

Of these statements

✓

Answer

(ii) and (iii) are correct
Solution:

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°.
$\angle\text{AOD}+\angle\text{DOB}=180^\circ$
$\angle\text{DOB}+\angle\text{BOC}=180^\circ$
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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