Question 827410
A quadrilateral is a polygon with 4 sides.
For a polygon with {{{n}}} sides, the measures of the {{{n}}} angles add up to {{{(n-2)*180^o}}} .
The measures of the 3 angles of a triangle add up to {{{180^o}}} .
The measures of the 4 angles of a quadrilateral add up to {{{2*180^o=360^o}}} .
The measures of the 5 angles of a pentagon add up to {{{3*180^o=540^o}}} .
For your quadrilateral, the measures of the angles (in degrees) are
{{{y+11}}} , {{{y-4}}} , {{{y+13}}} , and {{{y}}} .
If you add them all up, it should equal {{{360}}} .
{{{(y+11)+(y-4)+(y+13)+y=360}}}
{{{y+11+y-4+y+13+y=360}}}
{{{y+y+y+y+11-4+13=360}}}
{{{(y+y+y+y)+(11-4+13)=360}}}
{{{4y+20=360}}}
{{{4y=360-20}}}
{{{4y=340}}}
{{{y=340/4}}}
{{{highlight(y=85)}}}
So the measure of one of the angles in your quadrilateral is {{{85^o}}} .
 
The measures (in degrees) of the other 3 angles are
{{{y+11=85+11=highlight(96)}}} ,
{{{y-4=85-4=highlight(81)}}} , and
{{{y+13=85+13=highlight(98)}}} .