Find missing angle
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  angles 1-8 are 62°, 71°, 109°, 35°, 109°, 29°, 47°, 62°

Step-by-step explanation:

It is convenient to make use of the relations ...

Using these relations, we have ...

  ∠2 = 71° (vertical angles)

  ∠3 = ∠5 = 180° -71° = 109°

  ∠1 +47° = ∠3 = 109°   ⇒   ∠1 = ∠8 = 62° (alt int angles)

  ∠4 +36° = 71°   ⇒   ∠4 = 35°

  ∠6 +42° = ∠2 = 71°   ⇒   ∠6 = 29°

  ∠7 = 47° (alt int angles)

There are other ways to work these, using the sum of angles in a triangle, for example.

In order, angles 1-8 are ...

  62°, 71°, 109°, 35°, 109°, 29°, 47°, 62°

horizontal translation of 2 units in the positive x direction

followed by

vertical translation of 3 units in the positive y direction