What you have been given IS a walkthrough on how to professionally solve it.
The largest triangle is isosceles, so angles 3 and 2 are equal. Since they're both 68, angle 1 must be 44 as the three angles add to 180.
To create the smaller triangles, the three angles are bisected. If we look at the left-most triangle, angle 3 is halved to give 34, angle 1 is halved to give 22. How do you get the third angle in this triangle if they all have to add to give 180?