Which angle in the figure is a right angle? A. ECF B. C C. DCE D. DCF

The angle DCF is the right angle (D.).

Step-by-step explanation:

Usually, the right angles are marked with a small square, so if you see that, it means that is a 90º angle, no questions asked. :]

Answer A. says ECF, but that is only one of the two angles that add up to make the 90º angle.

Answer B. is not an angle at all. They should come with a slanted L and 3 letters to indicate an angle.

Answer C. says DCE, but that is just the other angle that adds up to make the 90º angle.

So that means Answer D. is the correct answer!

D. DCF

Step-by-step explanation:

A right angle or 90 degree angle angle is denoted by a small square where two line segments or rays meet to create an angle.

Angle ECF is inside of the right angle, but it only makes up part of it.

Angle C is not an angle.

Angle DCE is also inside of the right angle, but only makes up part of it.

Angle DCF is the angle with a small square inside of it. Therefore, it must be the right angle.

D. DCF is the correct answer.

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.