Question

Given △ABC∼△DEF , m∠A=52° , and m∠E=11° , what is the measure of angle C ?

Answer 1

[AI-generated answer — Bot GPT 3.5]

Since the triangles are similar, the ratios of corresponding sides are equal. Therefore, we can set up the following proportion:

AB/DE = BC/EF = AC/DF

Since angle A measures 52° and angle E measures 11°, we can conclude that angle C and angle F are supplementary angles (angle C + angle F = 180°). Therefore, angle F measures 180° - 11° = 169°.

Let's denote the measure of angle C as x. We can now set up another proportion:

AB/DE = BC/EF

Since we know the measures of angles A and E, we can plug in their values:

(AB/DE) = (BC/EF)
(AB/DE) = (BC/DF)

We can now solve this proportion:

(AB/DE) = (BC/DF)
(BC/2) = x/(DF)
(BC/DF) = (BC/2)/169
(BC/DF) = (BC/2)*(1/169)
(BC/DF) = BC/338

Since the sides BC and DF are proportional, we can conclude that their ratios are equal:

BC/338 = BC/338

Therefore, x/(DF) = 1, which means:

x = DF

Since the measure of angle F is 169°, we can conclude that the measure of angle C is also 169°.

Therefore, the measure of angle C is 169°.