Question

# Which statement is true by angle addition postulate?

a. πβ π΄ππ΅ + πβ πΆππ· = πβ π΄ππ·

b. πβ π΄ππ΅ + πβ π΅ππ = πβ π΄ππ

c. πβ π΅ππ + πβ πΆππ· = πβ π΅ππ·

## The correct answer is: 2 is true

- Step by step explanation:Β
- Step 1:
- given

πβ π΄ππ΅ + πβ πΆππ· = πβ π΄ππ·

From above figure, it is clear that

πβ π΄ππ΅ + πβ πΆππ· does not make complete angle.

Β β΄ πβ π΄ππ΅ + πβ πΆππ· = πβ π΄ππ·

- Step 2:Β

πβ π΄ππ΅ + πβ π΅ππ = πβ π΄ππ

From above figure, it is clear that

πβ π΄ππ΅ + πβ π΅ππ = πβ π΄ππ

β΄ πβ π΄ππ΅ + πβ π΅ππ = πβ π΄ππ

- Step 3:

πβ π΅ππ + πβ πΆππ· = πβ π΅ππ·

From above figure, it is clear that

πβ π΄ππ΅ + πβ πΆππ· + πβ πΆπ*P* = πβ π΄ππ·.

Β β΄ πβ π΅ππ + πβ πΆππ· = πβ π΄π

- Final Answer:

Hence, statement 2 is true.

- Step 1:
- given

From above figure, it is clear that

πβ π΄ππ΅ + πβ πΆππ· does not make complete angle.

From above figure, it is clear that

From above figure, it is clear that

*P*= πβ π΄ππ·.