Given: ABCD is an inscribed polygon.

Prove: ∠A and​∠C​ are supplementary angles.

Figure shows a circle with center point O. Point A, point B, point C, and point D are located clockwise on the circle. Segment A B, segment B C, segment C D, and segment D A are shown.


Drag an expression or phrase to each box to complete the proof.

Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Statement Reason
​ABCD is an inscribed polygon. Given
mBCD=2(m∠A) Response area
mDAB=2(m∠C) Inscribed Angle Theorem
mBCD+mDAB=360° Response area
2(m∠A)+2(m∠C)=360° Response area
​m∠A+m∠C=180°​ Division Property of Equality
​​ ∠A and​∠C​ are supplementary angles. Response area