Given, ∠BPT=28∘,PT= tangent, AB= Diameter In △OCP, ∠OCP+∠CPO+∠COP=180∘ 90∘+28∘+∠COP=180∘ [∵∠OCP=90∘] ⇒∠COP=180∘−90∘−28∘ ∠COP=62∘ where OC is perpendicular to tangent PT. In △OCB,OC=OB= radius so, ∠OCB=∠OBC ⇒∠OCB+∠CBO+∠BOC=180∘ ⇒2∠OCB=180∘−∠BOC =180∘−62∘ ⇒2∠OCB=118∘ ⇒∠OCB=59∘ In △OCP,∠OCB+∠BCP=∠OCP ⇒59∘+x∘=90∘ ⇒x∘=90∘−59∘ x∘=31∘=∠BCP