Two angles are supplementary. if the m∠a is five times the sum of the m∠b plus 7.2°, what is m∠b? need

Definition of supplementary angles:

Two Angles are Supplementary when they add up to 180 degrees. Notice that together they make a straight angle.

m∠A +m∠B =180°(1)

We are given :

m∠A is five times the sum of the m∠B plus 7.2°

m∠A = 5(m∠B +7.2) (2)

Plugging value of angle A from equation (2) in (1),

5(m∠B +7.2) + m∠B =180

5m∠B +36 + m∠B =180

6m∠B =180-36

m∠B = 24°

So angle B is 24 degrees.

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.