WAEC Mathematics 2021 Theory — Question 22

Model answer

Join AC. ∠DCA=90° (angle in a semicircle, using diameter AD... taken from the diagram), so ∠CAD=180°-90°-50°=40°. Since ABCD is a cyclic quadrilateral, ∠ADC+∠ABC=180° → ∠ABC=130°. In isosceles ΔABC (|AB|=|BC|), ∠BAC=∠BCA=(180°-130°)/2=25°. Therefore ∠BAD=∠CAD+∠BAC=40°+25°=65°.