We solve as follows:
*Since angles 1 & 3 are opposite to congruent sides, then they are congruent too. Also, since their opposite by the vertex angles are also opposite to congruent sides we can determine that angles 1 & 3 are both equal to 90°.
Using the previous information, we determine angle 2:
37° + 90° + m<2 = 180° => m<2 = 53°
So, angle 2 has a measure of 53°.
Now, we proceed as follows:
*Since both triangles [Upper one and lower one] are congruent by SSS, then we have that angle 5 has a measure of 37° and therefore angle 4 has a measure of 53°.
In order:
m<1 = 90°
m<2 = 53°
m<3 = 90°
m<4 = 53°