Answer:
x = 75° and y = 105°
Step-by-step explanation:
In the given figure
- There are two parallel lines intersected by another line which called a transversal
- There are two corresponding angles formed from this situation
∵ The angle of measure (180 - x) and the angle of measure y are
corresponding angles
∵ Corresponding angles are equal in measures
→ Equate their measures
∴ 180 - x = y ⇒ (1)
- The down line and the transversal formed a pair of linear angles at the point of intersection
∵ The angle of measure y and the angle of measure 75° are linear angles
∵ The sum of the measures of the linear angles is 180°
→ Add their measures and equate the sum by 180°
∴ y + 75 = 180
→ Subtract 75 from both sides to find y
∵ y + 75 - 75 = 180 - 75
∴ y = 105°
→ Substitute the value of y in (1)
∵ 180 - x = 105
→ Subtract 180 from both sides
∵ 180 - 180 - x = 105 - 180
∴ - x = - 75
∵ Divide both sides by -1 to find x
∴ x = 75°
