Answer:
[tex] x =15[/tex]
Step-by-step explanation:
In [tex] \odot D, [/tex] AB and AC are chords which are equidistant from the center of the circle.
[tex] \therefore Chord \: AB \cong Chord\: AC[/tex]
[tex] \therefore m \widehat {AB} = m\widehat {AC} [/tex]
(Equal chords intercept equal arcs)
[tex] \because m \widehat {AB} = (10x-23)\degree [/tex]
[tex] \therefore m \widehat {AC} = (10x-23)\degree [/tex]
[tex] m \widehat {AB} +m \widehat {AC} +106\degree = 360\degree [/tex]
(Arc sum postulate of a circle)
[tex] (10x-23)\degree + (10x-23)\degree= 360\degree- 106\degree [/tex]
[tex] 2(10x-23)\degree = 254\degree [/tex]
[tex] (10x-23)\degree = 127\degree [/tex]
[tex] 10x-23 = 127 [/tex]
[tex] 10x = 127+23 [/tex]
[tex] 10x = 150 [/tex]
[tex] x = \frac {150}{10}[/tex]
[tex] x =15[/tex]
