Answers:
Problem 1 is x = 20
Problem 2 is x = 20
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Work Shown for problem 1 (on the left)
0.5*((x+50) + (6x-70)) = 3x
0.5*(7x-20) = 3x
3.5x-10 = 3x
3.5x-3x = 10
0.5x = 10
x = 10/0.5
x = 20
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Work Shown for problem 2 (on the right)
0.5*( (2x+10)+(4x) ) = 65
0.5*(6x+10) = 65
3x+5 = 65
3x = 65-5
3x = 60
x = 60/3
x = 20
It is a coincidence that we got the same result as before.
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Step-by-step explanation:
The two chords of a circle intersect at a point that is not necessarily the center of the circle. The chords form two opposite arcs. Adding up the arc measures and dividing by 2 will give the angle between the chords.
The formula is
C = (A+B)/2
where A and B are the arc measures. C is the angle between the arcs. Dividing by 2 is the same as multiplying by 0.5