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∠1 = 37°

∠2 = 127°

∠3 = 23°

Step-by-step explanation:

From the picture, we can see the following

∠1 + 90° + 53° = 180°

From this we now that...

∠1 = 180° - 90° - 53°

∠1 = 37°

Also, we can see that...

∠1 + ∠3 + 90° + 30° = 180°

Substatute ∠1 and then find ∠3

∠1 + ∠3 + 90° + 30° = 180°

37° + ∠3 + 90° + 30° = 180°

∠3 = 180° - 90° - 30° - 37°

∠3 = 23°

And the last thing we can see is that...

∠2 + 53° = 180°

∠2 = 180° - 53°

∠2 = 127°

So ...

∠1 = 37°

∠2 = 127°

∠3 = 23°