Question 940649

A quadrilateral angles of {{{(3x)}}}°, {{{(x+14)}}}°, {{{(2x+5)}}}°, {{{(4x+1)}}}°. 

to find the measure of the largest angle, first find {{{x}}}

as you know the sum of all angles in a quadrilateral is {{{360}}}°

so, we have:

{{{3x+(x+14)+(2x+5)+(4x+1)=360}}}

{{{3x+x+14+2x+5+4x+1=360}}}

{{{10x+20=360}}}

{{{10x=360-20}}}

{{{10x=340}}}

{{{x=340/10}}}

{{{x=34}}}

now find angles:

{{{(3x)}}}°=> {{{(3*34)}}}°=> {{{102}}}°
{{{(x+14)}}}° => {{{(34+14)}}}° => {{{48}}}°
{{{(2x+5)}}}° => {{{(2*34+5)}}}°=> {{{73}}}°
{{{(4x+1)}}}° => {{{(4*34+1)}}}°=>{{{137}}}°

so,the measure of the largest angle is {{{highlight(137)}}}°