Vertically Opposite Angles


 
 
Concept Explanation
 

Vertically Opposite Angles

Vertically Opposite Angles:

 

When two lines intersect they form two pairs of opposite angles, A + C and B + D. Another word for opposite angles are vertical angles. Vertical angles are always congruent, which means that they are equal.Two angles are said to be supplementary when the sum of the two angles is 180°.figure51

Example: In the given figure lines AB and CD intersect eah other at point O. If large angle AOD:angle DOB=7:11, find all the other angles.

Solution

Here,     large angle AOD+angle DOB=180^{circ}.  As large angle AOD:angle DOB=7:11,  Let the common factor be x

  large angle AOD=7x  and  large angle DOB=11x    [ As their ratio are given ]

So, 7x + 11x = 180, 18x = 180 and x = 10

large Rightarrow ;;angle AOD = 7times10=70^{circ},angle DOB=11times10=110^{circ}

    large angle BOC=angle AOD=70^{circ}      [ Vertically opposite angles ]

    large angle AOC=angle DOB=110^{circ}   [ Vertically opposite angles ]

Sample Questions
(More Questions for each concept available in Login)
Question : 1

Which of the following pairs represents vertically opposite angles?

Right Option : C
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Explanation
Question : 2

If two straight lines interscet, the measures of the vertically opposite angles are____.

Right Option : A
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Explanation
Question : 3

In the given figure, if angle AOC+angle BOC+angle BOD=338^{0} . Find all the four angles. 

Right Option : C
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Explanation
 
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