Angle A = 34°
Because we know that angle AEB and BED are equal to 90°
And we know angle EBC is bisected by line BD which means the angle measures of EBD and BDC are congruent.
First we need to figure out the angles in the triangle on top, triangle EBD and we already know 2 angle measures know, 28° and 90° so we subtract those two numbers from 180 to get 62°
(The reason we subtract from 180 is because the angle measure of a triangle all together equal 180)
And based on what we said earlier (the angle measures of EBD and BDC are congruent.) the angle EBD and BDC are both equal to 62°. This means angle EBC is equal to the sum of 62 and 62, 124°. And EBC + EBA= 180° because it’s a straight angle. So to get angle EBA we subtract 124 from 180 to get 56°.
Now we can find a we just need to subtract 56 and 90 from 180, when we do that we get 34 which means that angle A is 34°