Answer:
Corresponding Angles Theorem
When a straight line intersects 2 parallel lines, the angles in the same relative position are congruent (equal).
Alternate Exterior Angles Theorem
When a straight line intersects 2 parallel lines, the alternate exterior angles are congruent (equal).
Vertical Angle Theorem
When two straight lines intersect, the vertical angles are congruent (equal).
Part A
Q1. As s ║ c we can apply the Corresponding Angles Theorem:
⇒ 11x - 5 = 116
⇒ 11x - 5 + 5 = 116 + 5
⇒ 11x = 121
⇒ 11x ÷ 11 = 121 ÷ 11
⇒ x = 11
Q2. As s ║ c we can apply the Alternative Exterior Angles Theorem:
⇒ 12x - 4 = 148
⇒ 12x - 4 + 4 = 148 + 4
⇒ 12x = 152
⇒ 12x ÷ 12 = 152 ÷ 12
⇒ x = 38/3 = 12.7 (nearest tenth)
Part B
Q1. As j ⊥ r then the sum of the angles is 90°
⇒ 4x + 6x + 10 = 90
⇒ 10x + 10 - 10 = 90 - 10
⇒ 10x = 80
⇒ 10x ÷ 10 = 80 ÷ 10
⇒ x = 8
Q2. As j ⊥ r we can apply the Vertical Angles Theorem:
⇒ 5x - 10 = x + 70
⇒ 5x - 10 + 10 = x + 70 + 10
⇒ 5x = x + 80
⇒ 5x - x = x + 80 - x
⇒ 4x = 80
⇒ 4x ÷ 4 = 80 ÷ 4
⇒ x = 20