Angles on a Straight Line


 
 
Concept Explanation
 

Angles on a Straight Line

If the sum of two adjacent angles is large 180^{circ}, they are said to form a linear pair.

large angle AOB  and large angle BOC are linear pair of angles and their sum is large 180^{circ} i.e.,  large angle AOB+angle BOC = 180^{circ}

Illustration :  In the following figure large 40^{0}; and; 140^{^{0}} are adjacent angles.Whether they form a linear pair or not and name the straight line if formed ?

Solution: As 140+40 = 180 Hence the given pair forms a pair of linear angles and AOC is a straight line.

Illustration : It is given that large angle XYZ=64^{circ}  and XY is produced to a point P. Draw a figure from the given information. If ray YQ bisects large angle ZYP, find large angle XYQ  and reflex large angle QYP.

Solution:  It is given that ray YQ bisects large angle ZYP.  SO, let       

large angle PYQ=angle QYZ=x

 large Rightarrow ;;angle PYZ=2x 

large angle ZYX=64^{0}

Since QY stands on ray PX. 

 large therefore ;angle PYZ+angle ZYX=180^{circ}                (Linear Pair)

2x + 64 = 180 

2x = 180 - 64

2x = 116

hence x = 58.

large therefore ;;angle XYQ=angle XYZ+angle ZYQ=64^{circ}+58^{circ}=122^{circ}

and,   reflex large angle QYP=360^{circ}-angle QYP=360^{circ}-x=360^{circ}-58^{circ}=302^{circ}

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

The value of x in the following figure is

Right Option : C
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Explanation
Question : 2

What value of 'x' will make POQ a straight line.

Right Option : C
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Explanation
Question : 3

In the given figure,AOB is a straight line.Find the value of 21y+3x .

Right Option : A
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Explanation
 
 
 
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