The following figures are not drawn to scale but AB and CD are straight lines. Find x:

angle AOD + 170=180 (sum of angles on a straight line)

angle AOD=180-170

angle AOD=10

Angle BOC(4x)+ 170= 180 (sum of angles on a straight line )

angle BOC(4x) =180-170

4x=10

4x/4=10/4

x=2.5

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.

i understand 100% 10/10 hit or miss?

step-by-step explanation: