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Given: Quadrilateral ABCD is inscribed in circle O.

Prove: m∠A + m∠C = 180º

https://static.k12.com/nextgen_media/assets/8093697-NG_GMT_SemB_10_UT_08.png

 

**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
 #1
avatar+90023 
+2

Inscribed Angle Theorem

 

Correct

 

Correct  !!!!!

 

 

cool cool cool

CPhill  Mar 7, 2018

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