Given the two triangles shown, find the value of x

Here is the information shown in the diagram: in triangle ABC, Angle A = 68, Angle C = 38, AB = 6, and BC = 10. In triangle DEF, Angle D = 38, Angle E = 74, EF = 15, and DE = x.)

The value of x is (Choose...4, 11, 12, 19, 20, 25).

To solve this, we notice that the sum of the angle measures mentioned is 68 + 38 + 74 = 180. Thus Triangles ABC and FED are similar by AA Similarity. It remains only to set up the proportion:

DE/CB = EF/BA

x/10 = 15/6

x = 150/6 = 25

vintechnology vintechnology · Answer 2 · 2022-01-25T14:35:55+01:00

The value of x in the triangle is 25

The triangle are similar.

What are similar triangles:

Similar triangles are only different in sizes. There corresponding angles are equal and all corresponding side have the same ratios.

Therefore, let's find the value x by establishing the proportion below:

ΔABC ≅ ΔFED

AB / FE = BC / ED = AC / FD

6 / 15 = 10 / x

cross multiply

6x = 150

x = 150 / 6

x = 25

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