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

Gas mileage actually varies slightly with the driving speed of a car (as well as with highway vs. city driving). suppose your car averages 33 miles per gallon on the highway if your average speed is 54 miles per hour, and it averages 22 miles per gallon on the highway if your average speed is 75 miles per hour. answer parts (a) and (b) below. a. what is the driving time for a 2000-mile trip if you drive at an average speed of 54 miles per hour? what is the driving time at 75 miles per hour? the driving time at 54 miles per hour is nothing hours. (type an integer or decimal rounded to two decimal places as needed.) the driving time is at 75 miles per hour is nothing hours. (round to two decimal places as needed.) b. assume a gasoline price of $3.33 per gallon. what is the gasoline cost for a 2000-mile trip if you drive at an average speed of 54 miles per hour? what is the gasoline cost at 75 miles per hour? the gasoline cost at 54 miles per hour is $ nothing. (round to two decimal places as needed.) the gasoline cost at 75 miles per hour is $ nothing. (round to two decimal places as needed.)