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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