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.