Geometry: find the value of x. Round to the nearest tenth. How do I do this? screenshot attached

Step-by-step explanation:

To solve for x, remember the right triangle trigonometry ratios (soh-cah-toa).

If we look at the angle given (θ), then we see that 36 is adjacent or next to the 70° angle. x is the hypotenuse because it is opposite the right angle. So, we have to use cosine (adjacent and hypotenuse).

Cross multiply. (Multiply the first numerator by the second denominator. Then, multiply the first denominator by the second numerator).

Since we want to solve for x, we must isolate the variable. Divide both sides by the cosine of 70.

Round to the nearest tenth. The 5 in the hundredth place tells us to round the 2 to a 3.

x is about 105.3

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.