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In the given the figure above, m∠BAC = 64° and m∠CBA = 56°.
Part I: Find the m∠DEC.
Part II: Explain the steps you took to arrive at your answer. Make sure to justify your answer by identifying any theorems, postulates, or definitions used.

In the given the figure above mBAC 64 and mCBA 56 Part I Find the mDEC Part II Explain the steps you took to arrive at your answer Make sure to justify your ans class=

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musiclover10045

since the triangles are similar

angle DEC = 60 degrees


3 angles inside a triangle equal 180 degrees

BAC = DCE = 64

CBA = EDC = 56

DEC = 180 -56 -64 = 60 degrees


used angle-angle theorem

[tex]\text{Answer: }\angle DEC=60\textdegree[/tex]

Explanation:

Since we have given that

m∠BAC = 64° and m∠CBA = 56°

and AB║CD and BC║DE

First, we consider Δ ABC,

As we know two angles of a triangle so we need to find the third angle, for which we'll use the "Angle Sum Property",

Angle Sum Property, states that the sum of three angles of a triangle is  [tex]180\textdegree[/tex]

Now, we will apply this,

[tex]\angle BAC+\angle ABC+\angle ACB=180\textdegree\\\\64\textdegree+56\textdegree+\angle ACB=180\textdegree\\\\120\textdegree+\angle ACB=180\textdegree\\\\\angle ACB=180\textdegree-120\textdegree\\\\\angle ACB=60\textdegree[/tex]

Now, as we have given that

BC║DE

so,

m∠ACB=m∠DEC

(∵ Corresponding angles are equal for given parallel lines)

So,

[tex]\angle ACB=\angle DEC=60\textdegree[/tex]

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