If points A, D and C lie on a straight line, then angles ∠ADB and ∠BDC are supplementary angles and
[tex]m\angle ADB+m\angle BDC=180^{\circ}[/tex].
1. If you move point B right from the initial position, then m∠ADB increases and m∠BDC decreases, but [tex]m\angle ADB+m\angle BDC=180^{\circ}[/tex].
2. If you move point B left from the initial position, then m∠ADB decreases and m∠BDC increases, but [tex]m\angle ADB+m\angle
BDC=180^{\circ}[/tex].
3. When point B lie on the line ADC, then:
a. Point B lies on the right hand from point D: [tex]m\angle ADB=180^{\circ} \\m\angle BDC=0^{\circ} [/tex];
b. Point B lies on the left hand from point D: [tex]m\angle ADB=0^{\circ} \\m\angle BDC=180^{\circ} [/tex].
4. When point B is reflected about the line ADC situation is the same as in parts 1 and 2.
Conclusion: [tex]m\angle ADB+m\angle BDC=180^{\circ}[/tex].
