In the diagram below, overline AE cong overline BE overline DE cong overline DC and m angle D=32^ . Find m angle A .

Step-by-step explanation:

since the triangle CDE is an isoceles triangle (the 2 legs DC and DE are equally), the 2 angles at its baseline CE are equal.

combined with the fact that the sum of all angles in a triangle is always 180 degrees we can therefore say :

180 = 32 + 2× base angle

148 = 2× base angle

base angle = 74 degrees.

the angle DEC is one of these base angles and therefore 74 degrees.

and because of the symmetry of angles of crossing lines, this is equal to the angle AEB.

the triangle AEB is also an isoceles triangle. the angle A is one of its base angles at the baseline AB.

so, the same principle as before :

180 = 74 + 2× base angle

106 = 2× base angle

base angle = 53 degrees.

so, angle A is 53 degrees.