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

Question

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] · Answer 1 · 2022-09-03T20:27:30+03:00

zepelin [54]3 years ago

5 0

Answer:

A

Step-by-step explanation:

inscribed angle

lesya [120] · Answer 2 · 2022-09-03T21:30:27+03:00

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!