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AlladinOne [14]
4 years ago
7

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 arriv

e at your answer. Make sure to justify your answer by identifying any theorems, postulates, or definitions used.

Mathematics
2 answers:
Alex17521 [72]4 years ago
6 0

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 

aleksandr82 [10.1K]4 years ago
4 0

Answer:

m\angle DEC=60^{o}

Step-by-step explanation:

We have been given a diagram of two triangles, in which line AB is parallel to CD and BC is parallel to DE.

We can see that \angle DCE is corresponding to \angle BAC as both angles are formed on the same side of parallel lines AB and CD and transversal AE, therefore,m\angle BAC=m\angle DCE.

We can see that \angle EDC is corresponding to \angle CBA as both angles are formed on the same side of parallel lines BC and DE and transversal AE, therefore, m\angle CBA=m\angle EDC.

Upon Substituting our given angle measures we will get,

64^{o}=m\angle DCE    

56^{o}=m\angle EDC  

Since the sum of all the angles of a triangle is always 180 degrees, therefore, we can find measure of angle DEC by equating the sum of angles of our given triangle with 180.

m\angle EDC+m\angle DCE+m\angle DEC=180^{o}

56^{o}+64^{o}+m\angle DEC=180^{o}

120^{o}+m\angle DEC=180^{o}

m\angle DEC=180^{o}-120^{o}

m\angle DEC=60^{o}

Therefore, the measure of angle DEC is 60 degrees.


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