1 Answer

Thesimm · Answer 1 · 2022-07-28T01:12:44+0000

Answer:

$m\angle SXW =113\degree$

Explanation:

In circle with center X, VS is diameter.

So
$\widehat {SWV}$ is a semicircular arc.

$\therefore m\widehat{SWV} = 180\degree$

$\therefore (12x+7)\degree + (21x +8)\degree = 180\degree$

$\therefore (33x+15)\degree = 180\degree$

$\therefore 33x+15 = 180$

$\therefore 33x = 180-15$

$\therefore 33x = 165$

$\therefore x =(165)/(33)$

$\therefore x =5$

$m\angle SXW =m\widehat{SW}$

(Measure of central angle is equal to the measure of its corresponding minor arc)

$m\angle SXW =(21x + 8)\degree$

$m\angle SXW =(21* 5+ 8)\degree$

$m\angle SXW =(105+ 8)\degree$

$m\angle SXW =113\degree$

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