1. is a central angle, therefore, the arc will have the same measurement as the angle. Set the equation:
Arc = Central Angle
2x - 7 = 47
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
First, add 7 to both sides of the equation:
2x - 7 (+7) = 47 (+7)
2x = 47 + 7
2x = 54
Next, divide 2 from both sides of the equation:
(2x)/2 = (54)/2
x = 54/2 = 27
27 is your answer.
2. is a inscribed angle, meaning that the angle measurement will be half of the arc. Set the equation:
212 = 2(13x - 24)
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
First, divide 2 from both sides of the equation:
(212)/2 = (2(13x - 24))/2
106 = 13x - 24
Next, add 24 to both sides of the equation:
106 (+24) = 13x - 24 (+24)
106 + 24 = 13x
130 = 13x
Finally, divide 13 from both sides of the equation:
(130)/13 = (13x)/13
x = 130/13
x = 10
10 is your answer.
3. is a central angle. The arc and the angle will, therefore, have the same measurement:
137 = 3x + 5
First, subtract 5 from both sides of the equation:
137 (-5) = 3x + 5 (-5)
137 - 5 = 3x
132 = 3x
Next, divide 3 from both sides of the equation to isolate the variable, x:
(132)/3 = (3x)/3
x = 132/3 = 44
44 is your answer.
4. is a inscribed angle. The arc will be twice the measurement of the angle.
86 = 2(2x + 3)
First, isolate the variable x by dividing 2 from both sides of the equation.
(86)/2 = (2(2x + 3)/2
43 = 2x + 3
Next, subtract 3 from both sides of the equation:
43 (-3) = 2x + 3 (-3)
40 = 2x
Finally, divide 2 from both sides of the equation:
(40)/2 = (2x)/2
x = 40/2 = 20
20 is your answer.
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