Kinds of Angles

Angle:

  • Angle is the basic figure in geometry which is formed when two rays meet at a common point.
  • It is basically denoted by <.
  • It is measured in degree.
  • The common point where the two rays meet is called as the vertex of the angle.
  • And each ray forming the angle is called as arm or side of angle.
  • Angle is the measure of rotation.

There are six types of angles on the basis of magnitude of the angle which are explained as follows.

1) Acute angle:

  • Acute angle is the angle whose measure is less than 900.
  • The following fig shows the acute angle.
  • The range of angle for acute angle is 10-890.

Zero angle: When the two arms forming the angle are overlapping on each other then that angle is zero angle.

In following figure we see that the arms AB and AC overlapping so the measure of angle between them is zero. Hence it is called as zero angle.

2) Right angle:

  • Right angle is the angle whose measure is exactly 900.
  • Also, a quarter circle measures the angle as 900.
  • The following figure shows the right angle in which the rays or arms forming the angle are perpendicular to each other.

3) Obtuse angle:

  • Obtuse angle is the angle whose measure is greater than 900 but less than 1800.
  • Thus, the range of angle for Obtuse angle is 900-1800.
  • The following figure shows the Obtuse angle formed by the two rays meeting at a common point.

4) Straight angle:

  • Straight angle is the angle whose measure is exactly 1800.
  • In straight angle the two rays forming straight angle are exactly opposite to each other as shown in following figure.
  • Also, the half circle measures the angle as 1800.

5) Reflex angle:

  • Reflex angle is the angle whose measure is greater than 1800 but less than 3600.
  • Hence the range of angle for reflex angle is between 1800-3600.
  • The following figure shows the reflex angle.

6) Full rotation angle:

  • The angle whose measure is exactly 3600 is called as the full rotation angle.
  • It consist of three right angles in it.
  • The complete circle measures the angle as 3600.
  • In full rotation angle the initial ray rotates from 00 and covers 3600 and again comes back to the same position as shown in following figure

On the basis of the direction of measuring the angle, the angles are classified as positive angle and negative angle.

1) Positive angles:

  • In geometry mostly we measure the angle in anticlockwise direction that angle is always taken as positive and it is also called as positive angle.
  • In Cartesian coordinate system, the angle we measures starts from +ve X- axis and follows the anticlockwise direction.
  • The following figure shows the measuring of positive angle.

2) Negative angle:

  • The angle which is measured in the clockwise direction is called as the negative angle.
  • In Cartesian coordinate system, if we measured the angle starting from +ve X-axis in clockwise direction then it is taken as negative and it is called as negative angle.
  • The measuring of negative angle is as shown in following figure.
  • In geometry, mostly the values of angle measured are taken as positive because these angles are measured in anticlockwise direction.

There are various pairs of angles which are named differently according to their orientation which are explained as below.

1) Adjacent angles:

  • Adjacent angles are the angles which are having a common vertex point and also one arm forming the angle is also common to them.
  • The following figure shows the adjacent angles. Here <ABD and <CBD are adjacent angles.
  • Because these angles are having a common vertex point B and a common arm as side BD.

2) Complementary angles:

  • Two angles are said to be complementary angles when the sum of their angles is exactly 900.
  • That means, complementary angles forms the right angle together.
  • The following figure shows the complementary angles which makes an angle of 900
  • But, the angles which are not together they can also make the complementary angles as shown in figure below.
  • Here, the <ABC = 300 and <PQR = 600 hence their sum is 900. Hence these are the complementary angles also.

Note:

In a right angle triangle, the sum of two angles other than right angle is also 900. Hence these angles are also complementary angles as shown in following figure.

3) Supplementary angles:

  • Two angles are said to be supplementary angles when the sum of their angles is exactly 1800.
  • The following figure shows the supplementary angles formed together, as the sum of their angles is exactly 1800.
  • But, the angles which are not together they can also make the supplementary angles as shown in figure below.
  • Here, <ABC=1200 and <PQR= 600. Thus these two angles are also the supplementary angles.

4) Linear angles:

  • The two angles are linear angles which are formed due to the intersection of two lines and sum of their angles must be 1800.
  • Thus, all the linear angles are adjacent angles but all adjacent angles are not linear angles.
  • Adjacent angles are linear angles only when the sum of their angles is 1800.
  • The following figure shows the linear angles which are adjacent angles also, having a common vertex point and also one arm is common to them.

5) Vertical angles:

  • When two lines crosses each other that means intersect at a common point then the angles which are the opposite pairs are called as vertical angles.
  • And the vertical angles are always equal.
  • In following figure we see that there are two pairs of vertical angles which are equal also.
  • And also, here there are linear angles and indirectly adjacent angles are also.

6) Corresponding angles:

  • When two parallel lines are crossed with a third line i.e. transversal, then the angles which are in matching corners are called as corresponding angles.
  • In the following figure, the two parallel lines AB and PQ are crossed by a transversal MN then the angles formed at matching corners are corresponding angles.
  • Here, 4 pairs of corresponding angles are formed which are as given below.

7) Alternate interior angles:

  • When two parallel lines are crossed with a third line i.e. transversal then the angles formed on the inner sides of parallel lines but on the opposite sides of transversal are called as alternate interior angles.
  • In the following figure, the two parallel lines AB and PQ are crossed by a transversal MN then the angles formed on the inner sides of parallel lines which are opposite to transversal are angle a and d, c and b are the alternate interior angles.

8) Alternate exterior angles:

  • When two parallel lines are crossed with a third line i.e. transversal then the angles formed on the outer sides of parallel lines but on the opposite sides of transversal are called as alternate exterior angles.
  • In the following figure, the two parallel lines AB and PQ are crossed by a transversal MN then the angles formed on the outer sides of parallel lines which are opposite to transversal are angle a and d, c and b are the alternate exterior angles.


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