Final answer:
To find the measure of angle CFD in isosceles triangle DEF with angle DEF measuring 68°, we subtract the sum of the base angles (68° each) from 180°, resulting in 44° for angle CFD.
Step-by-step explanation:
To find the measure of angle CFD in triangle DEF, which is an isosceles triangle, we need to use the properties of isosceles triangles and the given information. According to the question, angle DEF measures 68°. In an isosceles triangle, the base angles are equal, meaning that the measures of angles DFE and DEF are the same. So, angle DFE must also measure 68°.
Now, we know that the angles in a triangle always sum up to 180°. Therefore, to find the measure of angle CFD, which is the vertex angle of the isosceles triangle DEF, we can subtract the sum of the measures of the two equal base angles (DFE and DEF) from 180°:
180° - (68° + 68°) = 180° - 136° = 44°
Thus, the measure of angle CFD is 44°.