Question

What is the measure of angle A?

Answer 1

First you have to find the angle B (check attachment)

$B = 180^{\circ} - 137^{\circ} = 43^{\circ}$

Then you can find the last angle inside the triangle, which I'll call C

$C = 180^{\circ} - 102^{\circ} - 43^{\circ} = 35^{\circ}$

Now you can find angle A

$A = 180^{\circ} - C = 180^{\circ} - 35^{\circ} = 145^{\circ}$