circle questions

30 Draw AO and BO, then ∠PAO = ∠PBO = 90∠AOB = 360 - 180 - 50 = 130∠ACB = (360 - ∠AOB)/2 = 115 (D) 31 As ∠DAB = ∠BDC∠DAB + ∠BDC + ∠CDB + 90 = 180∠DAB = (90 - 38)/2 = 26 (B)33 ∠OCD = 90 => ∠COD = 50∠CBD = (180 - 130)/2 = 25 (B)34 Draw OB, OC∠ABE = 100 => ∠OBC = ∠OCB = 10So, ∠CDE = 180 - ∠DEC - ∠DCE= 180 - 60 - 80 = 40 (A) 35 ∠CAD = 58So, ∠DEF = 58As, ∠AEF = ∠AED - ∠DEF = 90 - 58 = 32 (D)