Angles are most basic structure of geometry. Many geometrical figures are classified on the basis of their angles. So learning special angles will be very interesting and of wide use. While learning special angles we will discuss about carious types of angles like right angles, acute angles, linear pair of angles, Vertically opposite angles etc. There are many angles having lot of special characters, those are covered under heading of learning special angles. Before we go for their properties and other special characters let see some of special angles.
special angles
These are the few angles, which can be taken as special angles.
Properties of Special Angles:
While learning about special angles we are manly concern with the properties of those.
(i) Linear Pair Of Angles: - Angles that are formed by one or more rays standing on the line at same point. Interesting result about these is that there sum is always equal to 180.
special angles 1
Here in above figure x and y are linear pair of angles
x + y = 180.
(i) Vertically opposite angles: - Vertically opposite angles are formed when two lines cross each other. Important result about these is that they are equal in measure.
For Example: -
Vertically opposite angles
1 = 2 [ vertically opposite angles ]
3 = 4 [ vertically opposite angles ]
These are the few special angles of geometry.
Question Based on Special Angles:
Q 1. Find the missing angle in below figure.
Example
Since the two angles are linear pair of angles.
x + 60 = 180
x = 180 - 60
x = 120
Q2 Find the missing angles in given figure.
EX 2
Since angle 120 and angle x are linear pair of angles.
x + 120 = 180
x = 180 - 120
x = 60
Also angles x and z are vertically opposite angles.
x = y
y = 60
Similarly angle y and 120 are vertically opposite angles