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

In the given figure, find the value of $frac{y}{2}$
A. 8	B. 7	C. 9	D. 4
Right Option : C
View Explanation

Question : 2

In the given figure find the value of m ?
A. $45^{0}$	B. $80^{0}$	C. $20^{0}$	D. $60^{0}$
Right Option : C
View Explanation

Question : 3

Find the measure of $angle LNM$ in the following figure.
A. $angle LNM=30^{0}$	B. $angle LNM=41^{0}$	C. $angle LNM=40^{0}$	D. $angle LNM=42^{0}$
Right Option : C
View Explanation

Chapters

Square and Square Root

Cube and Cube Roots

Time, Speed and Distance

Partnership and Mixture

Permutation and Combination

Introduction to Trigonometry

HCF And LCM

Number Theory

Rules For Divisibility

Problems On Boats And Stream

Mensuration

Profit Loss and Discount

Simple and Compound Interest

Surface Area and Volume

Content / Category

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Central Government Service

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Banking And Insurance

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MBA Entrance

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English Proficiency

Reasoning Proficiency

Computer Proficiency

Navodaya Entrance 6th & 9th

Sainik School Entrance

Andhra Bank

Class / Course

CAT

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