Question

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.

Answer 1

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 

Answer 2

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.