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

For which value of (a+b),ABC will be a straight line ?
A. $90^{0}$	B. $180^{0}$	C. $360^{0}$	D. $150^{0}$
Right Option : B
View Explanation

Question : 2

Find the measure of $angle AFB$ in the following figure
A. $angle ABF=30^{0}$	B. $angle ABF=35^{0}$	C. $angle ABF=40^{0}$	D. $angle ABF=60^{0}$
Right Option : A
View Explanation

Question : 3

Find the measure of angle $angle RTS$ in the following figure
A. $angle RTS=88^{0}$	B. $angle RTS=89^{0}$	C. $angle RTS=87^{0}$	D. $angle RTS=79^{0}$
Right Option : B
View Explanation

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