+327 Given: Quadrilateral ABCD is inscribed in circle O.
Prove: m∠A + m∠C = 180º
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**All bolded text are my answers, unbolded is was given**
Answer Choices Given:
Inscribed Angle Theorem
The sum of arcs that make a circle is 360º
Central Angle Theorem
m∠A + m∠B = 180º
m∠A + m∠C = 180º
m(arc)DAB = 2(m∠C)
| Statements | Reasons |
|---|---|
| Quadrilateral ABCD is incribed in circle O. | Given |
| m(arc)BCD = 2(m∠A) | Central Angle Theorem |
| m(arc)DAB = 2(m∠C) | Inscribed Angle Theorem |
| m(arc)BCD + m(arc)DAB = 360º | The sum of arcs that make a circle is 360º |
| 2(m∠A) + 2(m∠C) = 360º | Substitution Property |
| m∠A + m∠C = 180º | Division Preperty of Equality |
Thank You So Much!!!
