Question 1035845
A trapezoid (in some languages) is a quadrilateral with two parallel sides.
In general, all four angles could have different measures,
but the angles attached to each non-parallel side are supplementary,
meaning that their measures add up to {{{180^o}}} .
{{{drawing(300,200,-1,11,-1,7,
line(0,0,10,0),line(1,6,8,6),
arrow(1,0,5,0),arrow(1,6,5,6),
line(0,0,1,6),line(10,0,8,6),
locate(0.2,0.8,x),locate(1,6,180^o-x),
locate(9.4,0.8,y),locate(6,6,180^o-y)
)}}}
 
In this case, the acute angles have the same measure, {{{x=y}}} ,
and so do the obtuse angles, because it is an isosceles trapezoid.
 
{{{4x}}}= four times the measures (in degrees) of the acute angles;
{{{4x+5}}}= five more than the measures (in degrees) of the acute angles,
and the problem says that
{{{4x+5=180-x}}} ,
so all we have to do is solve that equation.
{{{4x+5=180-x}}}
{{{5x=175}}}
{{{x=175/5}}} ---> {{{x=175/5}}} ---> {{{x=35}}}
So the acute angles measure {{{highlight(35^o)}}} ,
and the obtuse angles measure {{{180^o-35^o=highlight(145^o)}}} .