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m<F = 79 degrees

Step-by-step explanation:

As per the given information;

m<E = 22, the triangle EDF (the one that is given in the picture) is isosceles (meaning that the sides are congruent).

In an isosceles triangle, (a triangle where the sides are congruent) the base angles (the angles opposite to the two congruent sides) are also congruent. One should also know, that in an isosceles triangle, like in any triangle, the sum of the measures of the angles equals 180 degrees.

Using this we can say that

m<D = m<F

To keep it simple while solving the problem, let's say that they have a value of x degrees.

So,

m<E + m<D + m<F =180

Subsitute

22 + x + x = 180

Simplify and inverse operations

22 + x + x = 180

-22              -22

2x = 158

/2     /2

x = 79

So the measure of <D and <F is 79 degrees.