starshooter1407 starshooter1407
  • 12-03-2018
  • Mathematics
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Quadrilateral ABCD is inscribed in a circle. Find the measure of each of the angles of the quadrilateral. Show your work.

Quadrilateral ABCD is inscribed in a circle Find the measure of each of the angles of the quadrilateral Show your work class=

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agamal91
agamal91 agamal91
  • 12-03-2018
sum of the angles of any quad =360
then y+(x+2)+(x-2)+(x-10) = y +3x -10 =360 (by adding both sides by 10)
y + 3x =370 ;.... eq 1
the sum of each two opposite sides in a quad inscribed in a circle =180
then (x+2)+(x-2)=180 
therefore 2x =180
therefore x=90  (sub in eq 1)
y+3*90 =y +270 = 370 (subtracting both sides by 270)
therefore y=100
then measure angle B=100 degrees
A=92 degrees
C=88 degrees
D=80 degrees
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