Question 830235
ANOTHER WAY TO THE SOLUTION:
The sum of the measures of the interior angles in a polygon with {{{n}}} sides is {{{(n-2)*180^o}}} .
In particular, the sum of the measures of the interior angles in a quadrilateral is {{{(4-2)*180^o=2*180^o=360^o}}} .
The angles at A, and H are congruent (they have the same measure), because a kite is symmetrical, so if {{{A}}} is the measure of those angles,
{{{A+135^o+A+53^o=360^o}}}
{{{2A+135^o+53^o=360^o}}}
{{{2A+188^o=360^o}}}
{{{2A=360^o-188^o}}}
{{{2A=172^o}}}
{{{A=172^o/2}}}
{{{highlight(A=86^o)}}}