Geometry Practice Test 3

OB = OD radius ∠1 = ∠4 Given ∠1 + ∠4 = ∠2 + ∠3 In ΔOBD, ∠1 + ∠4 + ∠5 = 180° In ΔBCD, ∠2 + ∠3 + ∠6 = 180° So, ∠1 + ∠4 + ∠5 = ∠2 + ∠3 + ∠6 ∠5 = ∠6 ∠5 = 180° - (∠1 + ∠4) ∠7 = $\frac{1}{2} \angle 5$ (Angle subtended by an arc at the center is double that of the angle subtended by it any point on the circle.) ∠7 + ∠6 = 180° (sum of opposite angles is 180° in a cyclic quadrilateral.) $\frac{1}{2} \angle 5$ + ∠5 = 180° $\frac{3}{2} \angle 5$ = 180° ∠5 = 180 × $\frac{2}{3}$ = 120° ∠BAD = ∠7 = $\frac{1}{2} \angle 5$ = $\frac{1}{2} \times 120$ = 60° ∠BAD = 60°