Question

IF RAY YM IS BISECTOR OF ANGLE XYZ AND RAY YN IS BISECTOR OF ANGLE MYZ. IF ANGLE XYN=45 then find angle XYZ?

Answer 1

Answer:

∠ XYZ  = 60°

Step-by-step explanation:

Let say ∠ XYZ  = 4A

YM is bisector of ∠ XYZ

=> ∠ XYM = ∠MYZ = (1/2)∠ XYZ

=> ∠ XYM = ∠MYZ = (1/2)4A

=>  ∠ XYM = ∠MYZ = 2A

YN is bisector of ∠MYZ

=> ∠MYN = (1/2)∠MYZ

=> ∠MYN = (1/2)2A

=> ∠MYN =  A

∠XYN = ∠XYM  + ∠MYN

=> ∠XYN = 2A + A

=>  ∠XYN = 3A

=> 3A = 45°

=> A = 15°

=> 4A = 60°

∠ XYZ  = 60°

Answer 2

Answer:

∠ XYZ  = 60°

Step-by-step explanation:

Let say ∠ XYZ  = 4A

YM is bisector of ∠ XYZ

=> ∠ XYM = ∠MYZ = (1/2)∠ XYZ

=> ∠ XYM = ∠MYZ = (1/2)4A

=>  ∠ XYM = ∠MYZ = 2A

YN is bisector of ∠MYZ

=> ∠MYN = (1/2)∠MYZ

=> ∠MYN = (1/2)2A

=> ∠MYN =  A

∠XYN = ∠XYM  + ∠MYN

=> ∠XYN = 2A + A

=>  ∠XYN = 3A

=> 3A = 45°

=> A = 15°

=> 4A = 60°

∠ XYZ  = 60°