CMI Entrance 2019 Problem from Transformation Geometry

Let's discuss a problem from CMI Entrance Exam 2019 based on the Inscribed Angle Theorem or Central Angle Theorem and Transformation Geometry.

The Problem:

Let $A B C D$ be a parallelogram. Let 'O' be a point in its interior such that $\angle A D B+\angle D O C=180^{\circ}$ . Show that $\angle O D C=\angle O B C$ .

The Solution:

Some useful resources:

Let's discuss a problem from CMI Entrance Exam 2019 based on the Inscribed Angle Theorem or Central Angle Theorem and Transformation Geometry.

The Problem:

Let $A B C D$ be a parallelogram. Let 'O' be a point in its interior such that $\angle A D B+\angle D O C=180^{\circ}$ . Show that $\angle O D C=\angle O B C$ .

The Solution: