Angle Addition Property

In this article we are going to discuss Angle Addition Property , the terms related to Angle Addition Property and some solved problems on Angle Addition Property .

Introduction to angle addition property :

The angle addition postulate states that if a point is within an angle and you add the two angles that are made by drawing a line through the point that the total will equal the large angle. ...




Angle Addition Property or postulate says that if there is a line segment SV lies in the interior of the angle TSR then Angle TSV + Angle VSR = Angle TSR

For example if Angle TSR = 40 degree and Angle TSV = 15 degree then the other angle will be of 25 degree.

The same property can be applied if there are two or more lines lies in the interior of an angle.

There are some important terms that are associated with Angle Addition Property

If two or more angle sums to 90 degree they are called complementary angles.



If two or more angles are lies in a straight line then definitely sums to 180 degree and called Supplementary Angle.



Two or more angles sharing same side are called Adjacent Angles.



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Lets Learn more about Angle Addition Property in Supplementary Angles



Supplementary Angles

What is the measure of Angle B if angle A is 120 degree?

Angle B + Angle A = 180

Angle B + 120 = 180

Angle B = 60 degree

Problem Based on Angle Addition Property.

Lets learn more about Angle Addition Property



Suppose Angle CAD is a complementary angle
‹CAB = 40 degree

‹EAD = 40 degree

‹BAE =  ?

Solution Angle CAB + Angle EAD + Angle BAE = Angle CAD
40 degree +40 degree + Angle BAE = 90
Angle BAE = 10 degree
What if I remove the line AB
calculate ‹CAE

Solution

‹CAE = 50 degree (‹CAB + ‹ BAE)

What if the three of the angle are of equal

Solution :Suppose each angle = x degree
X+x+x = 90
3x= 90
x= 30 degree
If Angle EAD is thrice to angle CAB

Angle BAE is 10 more to Angle CAB

Measure each angle

Let Angle CAB = x degree
Angle BAE = x+10 degree
Angle EAD = 3x
x+x+10+3x = 90
5x+10= 90
5x=80
x=16
Therefore Angle CAB ,BAE ,EAD are 16 ,26 ,48 degree respectively.