What is the measure of angle A?

First you have to find the angle B (check attachment)
[tex]B = 180^{\circ} - 137^{\circ} = 43^{\circ}\\[/tex]
Then you can find the last angle inside the triangle, which I'll call C
[tex]C = 180^{\circ} - 102^{\circ} - 43^{\circ} = 35^{\circ}[/tex]
Now you can find angle A
[tex]A = 180^{\circ} - C = 180^{\circ} - 35^{\circ} = 145^{\circ}[/tex]