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

Find the missing angle in the following diagram
A. 85 degrees	B. 69 degrees	C. 59 degrees	D. 38 degrees
Right Option : C
View Explanation

Question : 2

Find the measure of angle $angle ROQ$ in the following figure
A. $angle ROQ=81^{0}$	B. $angle ROQ=73^{0}$	C. $angle ROQ=83^{0}$	D. $angle ROQ=65^{0}$
Right Option : C
View Explanation

Question : 3

Two lines AB and CD intersect at O. if $angle AOC+angle COB+angle BOD=270^0$ Then find $angle AOD$ is ___________________
A. $70^0$	B. $80^0$	C. $90^0$	D. $180^0$
Right Option : C
View Explanation

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