Angle Addition Postulate defines that the if a position D lies in the inside of ∠ABC, then ∠ABD + ∠DBC = ∠ABC.

- An angle is supposed to be a complementary angle; If the sum of two angles are equal to 90° then it is known as complementary angle

- An angle is said to be supplementary angles then the sum of two angles must be equal to 180, then it is known as supplementary angle

- The angles which are sharing a same side are known as ‘adjacent angles’.

## Definition of Angle Addition Postulate

**Example 1:**

Find the *m*∠DBC [ ∠ABD = 50° and ∠ABC = 75° ]

**Solution:**

*m*∠ABD + *m*∠DBC = *m*∠ABC [ By Angle Addition Postulate.]

** **** **⇒ *m*∠DBC = *m*∠ABC – *m*∠ABD

Now we can substitute the given angles in the equation.

so, we get ⇒* **m*∠DBC = 75 – 50

*m*∠DBC = 25

The *m*∠DBC is found as 25^{o} by using the addition postulate.

## Example 2:

Find *m*∠DBC. [Given ∠ABD = 40° and ∠ABC = 70°.]

**Solution:**

*m*∠ABD + *m*∠DBC = *m*∠ABC [ By Angle Addition Postulate.]

** **⇒ ** ***m*∠DBC = *m*∠ABC – *m*∠ABD

Now we can substitute the given angles in the equation.

so, we get ⇒* **m*∠DBC = 70 – 40

*m*∠DBC = 30^{o}

The *m*∠DBC is found as 20^{o} by using the addition postulate.

**Example 3:**

**By using the angle addition postulate, find the missing angle in the given figure.**

** **

**Solution: **

**Here we have to find the missing angle (i.e.) x **

*m*∠SQR = X ( so we have to find *m*∠SQR )

from the given figure we can find the values of *m*∠PQS and *m*∠PQR.

*m*∠PQS = 35^{o} and *m*∠PQR = 85^{o}

By using the angle addition postulate we can find the missing angle (i.e. x)

*m*∠PQR = *m*∠PQS + *m*∠SQR

*m*∠PQR = *m*∠PQS + x

so, x = *m*∠PQR – *m*∠PQS

x = 85 – 35

x = 50^{o}

The missing angle x is found as 50^{o }by using the angle addition postulate.

## Practice Problems in addition postulate definition:

**Example 1:**Find the *m*∠DBC [ ∠ABD = 30° and ∠ABC = 95° ]

**Answer:65°**

**Example 2**:Find *m*∠DBC. [Given ∠ABD = 60° and ∠ABC = 80°.]

**Answer:20°**