∠adb and ∠bdc represent a linear pair because points a, d, and c lie on a straight line. calculate the sum of m∠adb and m∠bdc. then move point b around and see how the angles change. what happens to the sum of m∠adb and m∠bdc as you move point b around?

If points A, D and C lie on a straight line, then angles ∠ADB and ∠BDC are supplementary angles and
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1. If you move point B right from the initial position, then m∠ADB increases and m∠BDC decreases, but .
2. If you move point B left from the initial position, then m∠ADB decreases and m∠BDC increases, but .
3. When point B lie on the line ADC, then:
a. Point B lies on the right hand from point D: ;
b. Point B lies on the left hand from point D: .
4. When point B is reflected about the line ADC situation is the same as in parts 1 and 2.

Conclusion: .