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