Quadrilateral ABCD is inscribed in a circle. If angle A measures 85 degrees and angle D measures 80 degrees, what is the measure of: Angle B? Arc ADC?

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Answer 1 · 2018-01-28T04:40:27

Measure of #color(blue)(/_B = 100^0#

Arc Length #color(blue)(ADC = 3.49r)#

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In a cyclic quadrilateral, opposite angles add to 180

i.e. #/_A + /_C = 180, /_B + /_D = 180#

1) #:. /_B = 180 - /_D = 180 - 80 = color(blue)(100^0)#

Angle at the center is twice the angle at the circumference.

2) ARC length ADC will have angle #color(blue)(200^0)# at the center.

#:. Arc ADC = (X / 360) 2 pi r# where X is the angle subtended by the arc at the center and r the radius of the circle.

#Arc ADC = (200 / 360) * 2 * pi r = (10/9) pi r ~~ color(blue)(3.49r)#