Find the measure of angle 5.
measure of angle 7 = 2x+15
measure of angle 8 = 3x

x=33

Measure of angle 5=81

Measure of angle 6=99

Measure of angle 7=81

Measure of angle 8=99

Step-by-step explanation:

Angles 7 and 8 are supplementary because they share a common vertex while laying on a line.

That is the measurement of angles 7 and 8 add up to be 180.

mAngle7+mAngle8=180

(2x+15)  + (3x )        =180

 2x+15   + 3x           =180

Combine like terms:

 5x+15                      =180

Subtract 15 on both sides:

 5x                            =180-15

Simplify right hand side:

 5x                            = 165

Divide both sides by 5:

  x                             =165/5

Simplify right hand side:

  x                             =33

The measure of angle 7 is 2x+15=2(33)+15=66+15=81.

The measure of angle 8 is 3x=3(33)=99.

Recall vertical angles are congruent.

5 and 7 are vertical so the measure of angle 5 is 81.

6 and 8 are vertical so the measure of angle 6 is 99.

Measure of angle 5=81

Measure of angle 6=99

Measure of angle 7=81

Measure of angle 8=99

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.