Answer:
1. TRUE
2. TRUE
3. TRUE
4. TRUE
5. FALSE
6. TRUE
Step-by-step explanation:
1. From the diagram, we have that m∠2 and m∠7 are alternate interior angles
If m∠2 = 70° and m∠7 = 70°, then we have;
m∠2 = 70° = m∠7
m∠2 = m∠7
Therefore, the alternate interior angles of the lines l₁, and l₂ are equal, and therefore, the lines l₁ and l₂ are parallel, l₁ ║ l₂
TRUE
2. If m∠3 = 90° and m∠7 = 90°, therefore, the angle formed by the intersection of l₃ and l₂ = 90°
Therefore l₃ ⊥ l₂
TRUE
3. m∠5 and m∠7 are corresponding angles
If m∠5 = 85° and m∠7 = 85°, then, m∠5 = m∠7
Therefore, the corresponding angles formed by the lines l₁ and l₂ are equal, therefore;
l₁ ║ l₂
TRUE
4. Whereby we have, m∠1 = m∠5, we get;
m∠1 + m∠5 = 180° by sum of angles on a straight line
∴ m∠1 + m∠5 = m∠1 + m∠1 = 2·m∠1 = 180°
m∠1 = 180°/2 = 90°
∴ m∠1 = 90° = m∠5, and l₃ ⊥ l₁
TRUE
5. m∠1 and m∠8 are alternate exterior angles
If m∠1 = 98° and m∠8 = 82°
∴ m∠1 ≠ m∠8 and l₁ ∦ l₈
FALSE
6. Given that l₁║ l₂, then the angle formed between l₁ and l₃ will be equal to th angle formed between l₂ and l₃
Therefore;
If l₁║ l₂, and l₃ ⊥ l₁, then l₃ ⊥ l₂
(If l₁║ l₂, and l₃ is perpendicular to l₁, then l₃ is also perpendicular to l₂)
TRUE
