Angle, Types of Angles, Linear pair of angles, Vertically Opposite Angles

Angle

An angle is formed by the two rays with a common end point.

Interior and Exterior of an angle

Interior of an angle: The set of all points which lie inside an angle.
Exterior of an angle: The set of all points which lie outside an angle.

Types of angles

(i) Right Angle 

An angle whose measure is $90{}^\circ $.

(ii) Acute Angle

An angle whose measure is less than $90{}^\circ $.

(iii) Obtuse Angle

An angle whose measure is more than $90{}^\circ $ but less than $180{}^\circ $.

(iv) Straight Angle

 An angle whose measure is $180{}^\circ $.

(v) Reflex Angle

An angle whose measure is more than $180{}^\circ $ and less than $360{}^\circ $.

(vi) Complementary Angles

Two angles, the sum of whose measure is $90{}^\circ .$ Here,
$\angle PQS+\angle SQR=180{}^\circ $  i. e. $x{}^\circ +y{}^\circ =90{}^\circ. $

(vii) Supplementary Angles

Two angles, the sum of whose measure is $180{}^\circ $. Here,
$\angle PQS+\angle SQR=180{}^\circ $  i. e. $x{}^\circ +y{}^\circ = 180{}^\circ. $
 

Some angle relations

Adjacent Angles

Two angles are said to be adjacent angles if,

(i) they have the same vertex.
(ii) they have a common arm
(iii) uncommon arms are on either side of the common arm.
so, $\angle PQS and\angle SQR$ are adjacent angles.

Linear Pair of Angles

Two adjacent angles are said to form a linear pair of angles, if their non-common arms are two opposite rays.

Note:
(i) If a ray stands on a line, then the sum of the adjacent angles so formed is $180{}^\circ $.
(ii) If the sum of two adjacent angles is $180{}^\circ $ then their non-common arms are two opposite rays.
(iii) The sum of all the angles round a point is equal to $360{}^\circ $.

Vertically Opposite Angles

Two angles are called a pair of vertically opposite angles, if their arms form two pairs of opposite rays.

Note: If two lines intersect, then the vertically opposite angles are equal.



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