Answer:
1= 80
2= 35
3= 33
Step-by-step explanation:
First start by solving for angle 1. A triangle is always equal to 180 degrees so if you know triangle 1 has an angle equal to 69 degrees and another angle equal to 31 degrees then all you would need to do is add them up (this equals 100) and subtract that sum from 180 to find the difference (it's 80.)
Now that you know angle 1 is equal to 80 you can solve angle 2 and 3. When there are intersecting lines, the angles across from each other are always equal. So, it is safe to assume that the angle across from angle 1 is also 80 degrees. This will help us figure out the other angles in triangles 2 and 3. These four intersecting angles will equal 360, therefore because angle 1 and the angle across from it equal 80 degrees, then what we can do is add up 80+80 (which equals 160) then subtract that from 360 (which equals 200.) Because the two undetermined center angles are equal to each other, we can simply divide 200 by 2 to get 100.
Now that we know that triangle 2 has angles equal to 45 and 100 degrees, and triangle 3 has angles equal to 47 and 100 degrees, we can figure out what angles 2 and 3 are. To find angle 2 we will add 45 and 100 to get 145, then we'll subtract it from 180 like before to get 35. To find angle 3 we will add 47 and 100 to get 147, then we'll subtract it from 180 like before to get 33.
