Question

in the given figure AB is the diameter of circle such that angle PAB is 40°. find angle PCA​

Answer 1

Answer:

First Join PB

Then the figure will be something like this in the attached pic..

In △PAB

⇒  ∠PAB=40°     

[ Given ]

⇒  ∠BPA=90°   

[ angle inscribed in semi-circle ]

⇒  ∠PAB+∠PBA+∠BPA=180°

[ Angle sum property of triangle ]

∴   40°+∠PBA+90°=180°

∴   ∠PBA=180°−130°

∴   ∠PBA=50°

⇒  ∠PBA=∠PCA=50° 

[ angles inscribed in a same arc PA ] 

∴   ∠PCA=50°

Hope it helped you...

Thank you !!!