Me! in the figure shown, the measure of angle 6 is 141º. what is the measure of angle 5?

So lets look at the information we have:-

angle 6 = 141°
angle 5 = ? 

Angle 5 and angle 6 TOGETHER form a supplementary angle. A supplementary angle is equal to 180°. So, to find out angle 5 we will subtract 180° by angle 6 (141°). And then we will check our work. Lets do it:-

180° - 141° = 39°
Angle 5 = 39°

CHECK OUR WORK:-

39° + 141° = 180°
We were RIGHT!!! 

So, angle 5 measures 39°.

Hope i helped ya!!