1. ANGLEThe inclination between two rays having a common initial point is called an angle. The two rays forming an angle are called the arms (or) sides of the angle. The common end point of the two rays forming an angle is called the vertex of the angle. An angle is denoted by the symbol ‘ ∠ ’ In the above figure, the rays AB and AC form an ∠BAC or ∠CAB having ‘A’ as vertex and AB,AC as its arms. We may also denote this angle by ∠A . When there are more than one angles in a figure, we label them 1,2,3 etc. and call them ∠1,∠2,∠3 etc. Thus, in the above figure ∠BOA=∠1,∠COB=∠2 and ∠COD=∠3 Measuring Angles 2. TYPES OF ANGLES In the above figure, ∠ABC=50∘<90∘ Therefore ∠ABC is an acute angle Right Angle In the above figure, ∠ABC=900 Therefore ∠ABC is an right angle In the above figure, ∠ABC=1300Clearly 90° < 130° < 180° Therefore ∠ABC is an obtuse angle Straight Line Reflex Angle Complementary Angles • Complement of 400=900−400=500 Eg: • Supplement of 800=1809−80∘=100∘ In the given figure, ∠AOB and ∠BOC are adjacent angles, since they have a common vertex ‘O’. A common arm of OB and their other arms OA and OC are on the opposite sides of the common arm OB. In the above figure, ∠AOB and ∠BOC form a linear pair of angles as they have a common arm OB and their other arms OA and OC are opposite rays. Therefore ∠AOB+∠BOC=180∘ Thus, in the above figure, we have ∠1+∠2+∠3+∠4=180∘ Angles at a Point In the above figure, we have ∠1+∠2+∠3+∠4+∠5=360∘ Vertically Opposite Angles Let AB and CD be two lines intersecting at a point ‘O’. When two lines intersect, then vertically opposite angles are always equal. 3. PARALLEL LINES Transversal 4. ANGLES FORMED WHEN A TRANSVERSAL CUTS TWO LINES Two pairs of Interior alternate angles: (∠3,∠6) and (∠4,∠5) form two pairs of interior alternate angles. 1. Interior alternate angles are equal ∠3=∠6 and ∠4=∠5 5. CONDITION OF PARALLELISM OF TWO LINESIf two straight lines are cut by a transversal such that,• A pair of alternate angles are equal.• A pair of corresponding angles are equal • The sum of the interior angles on the same side of the transversal is two right angles, then the two straight lines are parallel to each other. Updated on April 21, 2021 |