Answered

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The center of the circle is G. Below is a student's work to find the
value of x. Explain the error and find the correct value of x.

The Center Of The Circle Is G Below Is A Students Work To Find The Value Of X Explain The Error And Find The Correct Value Of X class=

Sagot :

Answer:

The error are

1) The use of the angle addition postulate, for [tex]m \widehat{ACD}[/tex]

2) The assumption that [tex]m \widehat{BC}[/tex] = 90°

The vertical angle property between  [tex]m \widehat{CD}[/tex] and [tex]m \widehat{FA}[/tex] should be used to find 'x'

x = 5

Step-by-step explanation:

From the drawing of the circle, we are given;

AD = A diameter of the circle

∴ [tex]m \widehat{ACD}[/tex] = 180°

By angle addition postulate, we have;

[tex]m \widehat{ACD}[/tex] = [tex]m \widehat{AB}[/tex] + [tex]m \widehat{BC}[/tex] + [tex]m \widehat{CD}[/tex]

By substitution property of equality, we have;

180° = [tex]m \widehat{AB}[/tex] + [tex]m \widehat{BC}[/tex] + [tex]m \widehat{CD}[/tex]

[tex]m \widehat{AB}[/tex] = 5·x°

[tex]m \widehat{BC}[/tex] = Not given

[tex]m \widehat{CD}[/tex] = 15·x°

However;

[tex]m \widehat{CD}[/tex] is the vertically opposite angle to [tex]m \widehat{FA}[/tex]

∴  [tex]m \widehat{CD}[/tex] = [tex]m \widehat{FA}[/tex] = (16·x - 5)°

[tex]m \widehat{CD}[/tex] = 15·x° = (16·x - 5)°

15·x° = (16·x - 5)°

∴ 5 = 16·x° - 15·x° = x

x = 5

[tex]m \widehat{BC}[/tex] = 180° - ([tex]m \widehat{AB}[/tex] + [tex]m \widehat{CD}[/tex]) = 180° - (15·x° + 5·x°) = 180° - (20·x°)

[tex]m \widehat{BC}[/tex] = 180 - (20×5)° = 80°

[tex]m \widehat{BC}[/tex]  = 80°

The error are the use of the angle addition postulate, for [tex]m \widehat{ACD}[/tex], and the assumption that [tex]m \widehat{BC}[/tex] = 90° rather than the vertical angle property between  [tex]m \widehat{CD}[/tex] and [tex]m \widehat{FA}[/tex] in trying to find 'x', from which x = 5.

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