Geometry Problem 1491: Cyclic Quadrilateral, Diagonal, Incircle, Angle, Measurement

The figure shows a cyclic quadrilateral ABCD with the incircles O₁ and O₂ of the triangles ABC and ACD. If the measure of angle BAD is 80 degrees find the measure of angle O₁, O₂D.

See solution below

Incircle

Incircle is a circle within a triangle, that is tangent to each side.

Cyclic Quadrilateral

A cyclic quadrilateral is a quadrilateral whose vertices all lie on a single circle.