In a triangle ABC, CA is produced to P, ∠ BAP=126°. If ∠B : ∠C = 5 : 2, the degree measures of ∠B and ∠C are respectively :

90° and 36°

CP is a straight line.

So, ∠BAP + ∠CAB = 180º

∠CAB = 180º - 126º 

= 54º 

It is given that :- ∠B : ∠C = 5 : 2

In triangle ABC,

∠CAB + ∠BCA + ∠CBA = 180º

54º +  5a + 2a = 180º

7a = 126º

a = 18º

Now, ∠B = 5a = 5 × 18º  = 90º 

∠C = 2a = 2 × 18º  = 36º 

Answer :- 90º  and 36º