in exercises 5-6, find the measure of angle 1 through 5 in the figure shown

∠1 - 40°

b/c it's a right triangle and we have two angles given, 50° and 90°. Add them and subtract by 180° and get 40°.

∠2 - 140°

b/c an exterior (outside) angle is equal to the two most isolated / farthest angles added. The two most is angles are 105° and 35°, add them and get 140°.

∠3 - 40°

b/c ∠'s 1 and 3 are vertical angles meaning they're equal so since ∠1 is 40°, so is ∠3.

∠4 -

b/c ∠' s 2 and 4 are vertical angles meaning they're equal so since ∠2 is 140°, so is ∠4.

∠5 - 35°

b/c we have two angles, 105° and 40°. Add them and subtract by 180° and get 35°.

~~

I hope that helps you out!!

Any more questions, please feel free to ask me and I will gladly help you out!!

~Zoey