Answered

Discover a world of knowledge at Westonci.ca, where experts and enthusiasts come together to answer your questions. Join our platform to connect with experts ready to provide precise answers to your questions in various areas. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

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.

Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.