Answer:
[tex]m\angle DEC=60^{o}[/tex]
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 [tex]\angle DCE[/tex] is corresponding to [tex]\angle BAC[/tex] as both angles are formed on the same side of parallel lines AB and CD and transversal AE, therefore,[tex]m\angle BAC=m\angle DCE[/tex].
We can see that [tex]\angle EDC[/tex] is corresponding to [tex]\angle CBA[/tex] as both angles are formed on the same side of parallel lines BC and DE and transversal AE, therefore, [tex]m\angle CBA=m\angle EDC[/tex].
Upon Substituting our given angle measures we will get,
[tex]64^{o}=m\angle DCE[/tex]
[tex]56^{o}=m\angle EDC[/tex]
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.
[tex]m\angle EDC+m\angle DCE+m\angle DEC=180^{o}[/tex]
[tex]56^{o}+64^{o}+m\angle DEC=180^{o}[/tex]
[tex]120^{o}+m\angle DEC=180^{o}[/tex]
[tex]m\angle DEC=180^{o}-120^{o}[/tex]
[tex]m\angle DEC=60^{o}[/tex]
Therefore, the measure of angle DEC is 60 degrees.
