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∠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?

User Datazang
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2 Answers

4 votes

Answer:

The sum of m∠ADB and m∠BDC remains the same: m∠ADB + m∠BDC = 180°.

Explanation:

User Rodrigo Siqueira
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8.5k points
3 votes
If points A, D and C lie on a straight line, then angles ∠ADB and ∠BDC are supplementary angles and

m\angle ADB+m\angle BDC=180^(\circ).
1. If you move point B right from the initial position, then m∠ADB increases and m∠BDC decreases, but
m\angle ADB+m\angle BDC=180^(\circ).
2. If you move point B left from the initial position, then m∠ADB decreases and m∠BDC increases, but
m\angle ADB+m\angle BDC=180^(\circ).
3. When point B lie on the line ADC, then:
a. Point B lies on the right hand from point D:
m\angle ADB=180^(\circ) \\m\angle BDC=0^(\circ);
b. Point B lies on the left hand from point D:
m\angle ADB=0^(\circ) \\m\angle BDC=180^(\circ).
4. When point B is reflected about the line ADC situation is the same as in parts 1 and 2.

Conclusion:
m\angle ADB+m\angle BDC=180^(\circ).








User Miah
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8.1k points