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1. a || b Given

2. m<6 = ⅛m<4 Given

3. m<6 + m<4 = 180 Supplementary Angles

4. m<6 + 8<m6 = 180 Substitution

5. m<6 = 20; m<4 = 160 Algebra

Step-by-step explanation:

Required

Fill in the gaps

1. a || b Given

From the question, we understand that m<6 is ⅛ of m<4. This answers (2) as follows:

2. m<6 = ⅛m<4 Given

From the attached figure, m<6 and m<4 are supplementary angles and they add up to 180. So:

3. m<6 + m<4 = 180 Supplementary Angles

In (2): m<6 = ⅛m<4

Multiply both sides by 8

8 * m<6 = 8 * ⅛m<4

8m<6 = m<4

So, substitute 8m<6 for m<4 in (3). This gives (4)

4. m<6 + 8<m6 = 180 Substitution

Solve (4) algebraically,

9m<6 = 180

Multiply both sides by ⅑

⅑ * 9m<6 = ⅑ * 180

m<6 = 20

Recall that m<4 = 8m<6

So:

m<4 = 8 * 20

m<4 = 160

Hence, (5) is

5. m<6 = 20; m<4 = 160 Algebra

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.

stethere all not eveanp-by-step explanation: