Let the measure of Arc B C D = a°. Because Arc B C D and Arc B A D form a circle, and a circle measures 360°, the measure of Arc B A D is 360 – a°. Because of the ________ theorem, m∠A = StartFraction a Over 2 EndFraction degrees and m∠C = StartFraction 360 minus a Over 2 EndFraction degrees. The sum of the measures of angles A and C is (StartFraction a Over 2 EndFraction) + StartFraction 360 minus a Over 2 EndFraction degrees, which is equal to StartFraction 360 degrees Over 2 EndFraction, or 180°. Therefore, angles A and C are supplementary because their measures add up to 180°. Angles B and D are supplementary because the sum of the measures of the angles in a quadrilateral is 360°. m∠A + m∠C + m∠B + m∠D = 360°, and using substitution, 180° + m∠B + m∠D = 360°, so m∠B + m∠D = 180°.

What is the missing information in the paragraph proof?

Because the angles are inscribed in the circle, the angle lie on arcs which mean that the angles have to add up to 360 degrees just like a circle is 360 degrees, making it a quadrilateral that is inscribed!

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andromache andromache · Answer 2 · 2022-04-14T13:05:35+02:00

The missing information in the paragraph proof should be considered as the Inscribed Angle.

What is Inscribed Angle?

In terms of geometry, an inscribed angle should be the angle that should be created in the interior of a circle at the time when two chords intersect on the circle. Since the angles should be inscribed in the circle so here the angles should be added up to the 360 degrees same as like the circle also at the same time it should make the quadrilateral

Therefore, The missing information in the paragraph proof should be considered as the Inscribed Angle.

Learn more about an angle here: https://brainly.com/question/21103473