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Referring to the Figure, segment AB and segment NM are diametersof circle E. Find m∠BEN

Referring to the Figure, segment AB and segment NM are diametersof circle E. Find-example-1
User RojoSam
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1 Answer

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From the information given, segments AB and NM are the diameters of the circle. They are straight lines.

Recall, the angles formed on a straight line are called linear pairs and their sum is 180 degrees. This means that the sum of the angles on segment NM is 180 degrees. Thus,

angleMEA + angle AEC + angle CEN = 180

From the diagram,

angle MEA = 55

angle CEN = 65

Thus,

55 + angle AEC + 65 = 180

120 + angle AEC = 180

angle AEC = 180 - 120 = 60 degrees

Now, we would consider segment AB. It means that

angle AEC + angle CEN + angle BEN = 180

By substituting the values, we have

60 + 65 + angle BEN = 180

125 + angle BEN = 180

subtracting 125 from both sides, we have

angle BEN = 180 - 125

angle BEN = 55 degrees

User Sotn
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