I'm going to refer to the two separate triangles in this problem by their missing angles. So the smaller triangle is triangle 1, and the larger triangle is triangle 2.
Let's work on triangle 1 first.
We can easily find the supplementary angle to the 115 degree angle in the middle there, which is in triangle 1.
180 - 115 = 65
Now that we know two of the angles in the triangle, and we know that the sum of the interior angles in a triangle is 180, we can find our missing angle 1.
80 + 65 + <1 = 180
145 + <1 = 180
<1 = 35 degrees
Now let's go ahead and move on to triangle 2.
We can again find the supplementary angle to the 115 degree angle in the middle there, which is in triangle 2 also.
180 - 115 = 65
Then, we can use the same principle as we did with triangle 1 to find our missing angle 2 in triangle 2.
85 + 65 + <2 = 180
150 + <2 = 180
<2 = 30 degrees
Hope this helps!! :)
