Question 1193037
For a quadrilateral ABCD, the measures of its angles are given below.

{{{m<A = (x + 14)}}}°
{{{m<B = (2(x + 2))}}}°={{{(2x + 4)}}}°
{{{m<C =(3/2)x - 13}}}°
{{{m<D =(7/3)x-14}}}°

Find {{{x}}}.

{{{x + 14+2x + 4+(3/2)x -13+(7/3)x-14=360}}}

{{{3x + 3x/2+7x/3-9=360}}}.......both sides multiply by {{{6}}}

{{{ 18x+9x+14x-54=2160}}}

{{{ 41x=2160+54}}}

{{{ 41x=2214}}}

{{{ x=2214/41}}}

{{{x=54}}}


then, measures of angles are:

{{{m<A = x + 14=54+14=68}}}°
{{{m<B =2*54 + 4=112}}}°
{{{m<C =(3/2)54 - 13=68}}}°
{{{m<D =(7/3)54-14=112}}}°


also, since you have a quadrilateral you know that opposite angles are equal


then you can find the value of {{{x}}} this way:

<{{{A=C}}}
{{{x + 14=(3/2)x - 13}}}

{{{13 + 14=(3/2)x -x}}}

{{{27=x/2}}}

{{{x=54}}}