# Chapter 2 : Angles

### Topics covered in this snack-sized chapter:

#### Angle arrow_upward

• An Angle is a figure formed by two rays with the same initial point.
• The initial point is called the Vertex.
• The two rays are called the Arms of the angle.

• It is generally represented by a symbol .

• #### Types of Angles arrow_upward

###### Acute Angle

• An angle that measures between  and  is called an Acute angle.
• For example:  is an Acute Angle.

• ###### Obtuse Angle

• An angle that measures between  and  is called an Obtuse angle.
• For example:  is an Obtuse Angle.

• ###### Reflex Angle

• An angle that measures between  and  is called a Reflex angle.
• For example:  is a reflex angle.

• ###### Straight Angle

• An angle that measures exactly  is called a Straight Angle.
• Straight (or Flat) angles are formed when the legs are pointing in exactly opposite directions.
• The two legs then form a single straight line through the vertex of the angle.
• The measure of a flat angle is thus always 180°.

###### Complete Angle

• An angle that measures exactly  is called a Complete angle.

• ###### Right Angle

• An angle that measures exactly  is called a Right angle.
• For example:  is a right angle.

• #### Pair of Angles arrow_upward

 Angle Pair Property Adjacent Angles Angles that have a common vertex and a common arm but no common interior.  is adjacent to . Vertically Opposite Angles A pair of non-adjacent angles formed by the intersection of two straight lines. Each opposite pair are called vertically opposite angles and are always congruent.  For example: ∠AOC and ∠BOD are vertically opposite angles. Complementary Angles Two angles that add up to 90°. For example, the sum of ∠a and ∠b is 90°. Supplementary Angles Two angles that add up to 180°. For example, the sum of ∠a and ∠b is 180°.

#### Degree Measure of an Angle arrow_upward

• The standard unit of measurement of an angle is Degree.
• It is represented by symbol of “ .
• 1 Right Angle = 90°= 90 Degree
• 1 Degree = 60 Minutes

#### Transversal arrow_upward

• A transversal is a line that crosses at least two other lines.

• ###### Transversal Intersecting Non Parallel Lines

• Here AB is a transversal which intersects two non parallel lines PQ and RS.

• ###### Transversal Intersecting Parallel Lines

• Here AB is a transversal which intersects two parallel lines PQ and RS.

• #### Vertically Opposite Angles arrow_upward

• Vertical Opposite Angles are the angles opposite to each other when two lines cross.
• They are called “Vertical” because they share the same vertex.
• Here  are vertical opposite angles.
• For example, if a and d are vertical angles, the measure of both a and d will be same.

• #### Interior Angles of a Transversal arrow_upward

• Angles that are formed on the inside of the two lines are known as Interior angles.
• Here   are interior angles.

• #### Exterior Angles of a Transversal arrow_upward

• Angles that are formed on the outside of the two lines are known as Exterior angles.
• Here   are exterior angles.

• #### Corresponding Angles arrow_upward

• If two lines are parallel, the pairs of angles on the same side of the transversal if both lie either above the two lines or below the two lines.
• Two line are intersected by a transversal such that  .

• #### Alternate Interior and Exterior Angles arrow_upward

• Alternate Interior Angles are created where a transversal crosses two (usually parallel) lines.
• Each pair of these angles are inside the parallel lines, and on opposite sides of the transversal.
• In the diagram below   are Alternate Interior Angles.
• Alternate Exterior Angles are created where a transversal crosses two (usually parallel) lines.
• Each pair of these angles are outside the parallel lines, and on opposite sides of the transversal.
• And   are Alternate Exterior Angles.

• #### Theorems: Angles arrow_upward

###### Property 1

• For parallel lines, Pairs of alternate (interior or exterior) angles are equal.

• ###### Property 2

• For parallel lines, Pairs of corresponding angles are equal.

• ###### Property 3

• The sum of the interior (or exterior) angles on the same side of the transversal is.

• #### Angle Bisector arrow_upward

• A ray that divides an angle into two equal and adjacent angles is called as an Angle Bisector.
• Angle bisector divides the angle AXC into two equal parts such that

∠AXB = ∠BXC.

#### Thank You from Kimavi arrow_upward

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