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elena-14-01-66 [18.8K]
3 years ago
14

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?
Mathematics
2 answers:
zepelin [54]3 years ago
5 0

Answer:

A

Step-by-step explanation:

inscribed angle

lesya [120]3 years ago
4 0

Answer:

A. Inscribed Angle

Step-by-step explanation:

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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