Triangles ABC and DEF are similar. If ∠ABC = 101°and ∠BCA = 39°, find the measure of angle FDE.

Two triangles, ABC and DEF, similar. <ABC = 101° and <BCA = 39°. Find the angle of FDE!

40°

The sum of all triangle angle is 180°

101 + 39 = 140°

180 - 140 = 40°

So, the angle of FDE is 40°

Subject : Math

Class : 7th Grade (Junior High School)

Chapter : -

Categorization Code : -

Keywords : Angle of a triangle

geometry: triangles

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answers archive

call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

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