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.

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 is corresponding to as both angles are formed on the same side of parallel lines AB and CD and transversal AE, therefore,.

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

Upon Substituting our given angle measures we will get,

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.

Therefore, the measure of angle DEC is 60 degrees.

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3