Given △ABC ∼ △DEF, where m∠A = 52° and m∠E = 11°, what is the measure of angle C?
Since ∠A and ∠E are corresponding angles of the similar triangles, we can conclude that the ratio of the measure of ∠A to the measure of ∠E is equal to the ratio of the corresponding side lengths.
Therefore, we have:
m∠A/m∠E = AB/DE = BC/EF = AC/DF
Given that m∠A = 52° and m∠E = 11°, we can write this as:
52/11 = AC/DF
Now, we can find the measure of angle C by calculating:
52/11 = AC/DF
52/11 = AC/AC + CF
52/11 = 52/11 + CF
52 = 52 + 11CF
11CF = 0
CF = 0
Therefore, the measure of angle C is 0°.