**Given Information:**
- We are given that vectors 2a - 4b and 10a + 8b are perpendicular to each other.
- a and b are unit vectors.

**To Find:**
- We need to find the angle between vectors a and b.

**Solution:**

1. Let's start by finding the dot product of the given vectors:
- (2a - 4b) · (10a + 8b) = 0
- Using the distributive law, we expand the dot product:
20(a · a) - 40(a · b) + 16(b · b) = 0
- Since a and b are unit vectors, their dot products with themselves are equal to 1:
20 - 40(a · b) + 16 = 0
- Simplifying the equation further:
36 - 40(a · b) = 0

2. Next, we need to find the dot product of vectors a and b:
- a · b = (a · b)(|a||b|)
- Since a and b are unit vectors, their magnitudes are equal to 1:
a · b = (a · b)(1)(1)
Therefore, a · b = a · b

3. Substituting the value of a · b in the earlier equation:
36 - 40(a · b) = 0
36 - 40(a · b) = 0
40(a · b) = 36
(a · b) = 36/40
(a · b) = 9/10

4. The dot product of vectors a and b is given by:
(a · b) = |a||b|cosθ
Substituting the known values:
9/10 = (1)(1)cosθ
cosθ = 9/10

5. Finally, we can find the angle θ between vectors a and b using the inverse cosine function:
θ = cos^(-1)(9/10)
θ ≈ 25.84 degrees

**Answer:**
The angle between vectors a and b is approximately 25.84 degrees.