Question

Find the value of x.

Answer 1

Answer:

$x =15$

Step-by-step explanation:

In $\odot D,$ AB and AC are chords which are equidistant from the center of the circle.

$\therefore Chord \: AB \cong Chord\: AC$

$\therefore m \widehat {AB} = m\widehat {AC}$

(Equal chords intercept equal arcs)

$\because m \widehat {AB} = (10x-23)\degree$

$\therefore m \widehat {AC} = (10x-23)\degree$

$m \widehat {AB} +m \widehat {AC} +106\degree = 360\degree$

(Arc sum postulate of a circle)

$(10x-23)\degree + (10x-23)\degree= 360\degree- 106\degree$

$2(10x-23)\degree = 254\degree$

$(10x-23)\degree = 127\degree$

$10x-23 = 127$

$10x = 127+23$

$10x = 150$

$x = \frac {150}{10}$

$x =15$