Question 765942
Q:
Find the value of x in the figure below. Show all steps.
circle with two chords intersection; on one side of the circle the two chords sweep out a 101 degree arc and on the opposite side of the circle a 37 degree arc; the angle formed by one of these sweeps is 5 x minus 6 degrees
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A:
{{{drawing(300,300,-10,10,-10,10,circle(0,0,8), line(-8,0,8,0), line(8*cos(101*pi/180),8*sin(101*pi/180),8*cos(217*pi/180),8*sin(217*pi/180)), locate(-3,1.75,"5"), locate(-2.5,1.75,"x-6"), locate(6.5,7,101^o),  locate(-10,-1.5,37^o))}}}
5x - 6 = {{{(101 + 37)/2}}}
5x - 6 = 69
x = {{{(69 + 6)/5}}}
x = {{{highlight(15)}}}