Can a regular polygon have an interior angles of 169?​

No. The sum of all angles in any polygon cannot be 169.

Step-by-step explanation:

However, a particular angle measure can be 169.

No.

Step-by-step explanation:

If it is a regular polygon then the sum of its exterior angles add up to 360 degrees. The number of sides in such a polygon  = 360 / exterior angle.

Here each exterior angle = 180-169 = 11 degrees,

Now 11 is not a factor of 360 and if we try to find the number of sides we don't get a whole number, so the answer is NO.

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.

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