In △QOA,QO=OA= radius Then, ∠OQA=∠OAQ=x∘ In △OQB,QO=OB= radius Then, ∠OQB=∠OBQ=y∘ Now, ∠MAP=∠MAQ+∠QAO+∠OAP [linear angle] ⇒58∘+x+90∘=180∘⇒x=32∘ Now, ∠NBP=∠NBQ+∠QBO+∠OBP [linear angle] ⇒50∘+y+90∘=180∘⇒y=40∘ Now, ∠BQA=∠BQO+∠OQA =32∘+40∘=72∘ Then, ∠BOA=2×∠BQA [∵ Angle made on centre is double of angle made at circumference] =2×72∘=144∘ Now, In squareOBAP ∠O+∠A+∠P+∠B=360∘ ⇒∠APB=360∘−144∘−90∘−90∘=36∘