We are asked to find the values of three angles in the following image:
Notice that angle 3 is the easiest for us, since in the triangle on the left the two other angles are known.
We know that the addition of al three angles of a triangle must give 180, so we can solve for the unknown angle 3:
72 + 86 + angle3 = 180
158 + angle3 = 180
angle3 = 180 - 158
angle3 = 22 degrees
Now, let's work on the triangle on the right. We know that angles 3 and 4 are opposite by the vertex, so they must be equal.
Then angle4 = 22 degrees.
And finally we use the addition of the three angles in the triangle on the right to find angle 5:
22 + 70 + angle 5 = 180
92 + angle 5 = 180
angle5 = 180 - 92
angle5 = 88 degrees