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°