Mathematics, 14.06.2021 16:10 nefox8408
Given: quadrilateral ABCD inscribed in a circle
Prove: ∠A and ∠C are supplementary, ∠B and ∠D are supplementary
A circle is inscribed with quadrilateral A B C D.
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?
inscribed angle
polygon interior angle sum
quadrilateral angle sum
angle bisector
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Given: quadrilateral ABCD inscribed in a circle
Prove: ∠A and ∠C are supplementary, ∠B and ∠D are s...
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