Question

If two straight lines intersect, the measures of the vertically opposite angle are .................

• A. equal
• B. not equal
• C. cannot be determined
• D. none of these

Answer 1

Answer: (A)

$AB$ and $CD$ are two straight lines intersecting at $O$.

$\Rightarrow$ $\angle AOC+\angle AOD={180}^o$ [ Linear pair ] ---- ( 1 )

$\Rightarrow$ $\angle AOD+\angle BOD={180}^o$ [ Linear pair ] ---- ( 2 )

From ( 1 ) and ( 2 ), we get

$\Rightarrow$ $\angle AOC+\angle AOD=\angle AOD+\angle BOD$

$\therefore$ $\angle AOC=\angle BOD$

Similarly we can prove, $\angle AOD=\angle BOC$

$\therefore$ We have proved that, If two straight lines intersect, the measures of the vertically opposite angle are $equal.$