Question

Please help me to solve this problem ​

Answer 1

Answer: Q.(1)∠z=70°,∠x=30°, y=80°, Q.(2) ∠y=30°,∠z = 90°,∠x=60°.

Step-by-step explanation: Q.(1)

Given:

∠PAB=30°,∠QAC=80°

Find= ∠ABC=X,∠ACB=Y,∠BAC=Z

∠PAB=30°=∠ABC=X(alternate angle)

∠QAC=80°=∠ACB=Y(alternate angle)

so, the x=30° and y=80°

In Δabc

∠a+∠b+∠c= 180°( angles sum property)

∠z+∠x+∠y=180°

∠z+30°+80°= 180°

∠z= 180° -110°

∠z=70°

Q.(2) In Δabc

∠a+∠b+∠c= 180°( angles sum property)

∠y+90°+60°= 180°

∠y=180° -150°

∠y=30°

∠BCA=60°=∠PAC=x(alternate angle)

∠PAC+∠ABC+∠BAQ = 180°(Linear pair)

∠x+∠y+∠z = 180°

60°+30°+∠z = 180°

∠z= 180° - 90°

∠z = 90°