Question 880477
In all convex quadrilaterals, like these,
{{{drawing(300,200,-3,33,-2,22,rectangle(0,0,30,20))}}} {{{drawing(300,200,-3,33,-2,22,
line(0,0,27,0),line(30,18,27,0),
line(0,0,5,20),line(30,18,5,20))}}}
the measures of the interior angles add up to {{{360^o}}} .
If you know the measures of 3 of the angles, you can find the measure of the fourth angle.
 
You may know that your quadrilateral is a parallelogram because you were told,
or because it is drawn on grid/graph paper,
or because the figure indicates that opposite sides are parallel with little arrows like this:
{{{drawing(300,200,-3,33,-2,22,
line(0,0,25,0),line(30,20,25,0),
line(0,0,5,20),line(30,20,5,20),
arrow(0,0,12,0),arrow(1,0,13,0),
arrow(5,20,17,20),arrow(6,20,18,20),
arrow(0,0,3,12),arrow(25,0,28,12)
)}}} .
In that case, opposite angles in the parallelogram have equal measures,
and the measures of adjacent angles add up to {{{180^o}}} .
So for {{{drawing(300,200,-3,33,-2,22,
line(0,0,25,0),line(30,20,25,0),
line(0,0,5,20),line(30,20,5,20),
arrow(0,0,12,0),arrow(1,0,13,0),
arrow(5,20,17,20),arrow(6,20,18,20),
arrow(0,0,3,12),arrow(25,0,28,12),
locate(5.5,20.5,(5x+5)^o),locate(25.5,20.5,(2x)^o)
)}}} the equation you would use is {{{(5x+5)+2x=180}}} ,
but you would use {{{5x+5=2x}}} for {{{drawing(300,200,-3,33,-2,22,
line(0,0,25,0),line(30,20,25,0),
line(0,0,5,20),line(30,20,5,20),
arrow(0,0,12,0),arrow(1,0,13,0),
arrow(5,20,17,20),arrow(6,20,18,20),
arrow(0,0,3,12),arrow(25,0,28,12),
locate(5,20.5,(5x+5)^o),locate(21,3,(2x)^o)
)}}}