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!!!

KennedyPape
Mar 7, 2018