Final answer:
The measure of angle C in similar triangles is found by knowing that the sum of angles in a triangle is 180° and corresponding angles in similar triangles are equal. Given angles A and E, the remaining angle C is calculated to be 40°.
Step-by-step explanation:
To solve for the measure of angle C (mzC) in similar triangles ABC and DEF, where mzA = 104° and mZE = 36°, we should remember that corresponding angles in similar triangles have the same measure. Therefore, since mzA corresponds to mzD and mzE corresponds to mzB, angle C must correspond to angle F. In a triangle, the sum of the angles is always 180°. Our goal is to find the third angle in both triangles, which is angle C in triangle ABC and angle F in triangle DEF.
The sum of angles in a triangle is 180°:
180° - mzA - mzB = mzC
For triangle ABC:
180° - 104° - mzB = mzC
We also know that mzB = mzE in triangle DEF (since they are similar triangles), so mzB = 36°. Replacing mzB with 36°:
180° - 104° - 36° = mzC
40° = mzC
Therefore, the correct answer is b) 40°.