Answer:
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
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