Answer:
x = 20
y = 24
Explanation:
Corresponding Angles Postulate
When a straight line intersects two parallel straight lines, the resulting corresponding angles are congruent.
As line m is parallel to line n:
⇒ (3x - 19)° = (2x + 1)°
⇒ 3x - 19 = 2x + 1
⇒ 3x - 19 - 2x = 2x + 1 - 2x
⇒ x - 19 = 1
⇒ x - 19 + 19 = 1 + 19
⇒ x = 20
Linear Pair
Two adjacent angles that sum to 180° (two angles which when combined together form a straight line).
Therefore:
⇒ (5y + 19)° + (2x + 1)° = 180°
⇒ 5y + 19 + 2x + 1 = 180
Substitute the found value of x:
⇒ 5y + 19 + 2(20) + 1 = 180
⇒ 5y + 19 + 40 + 1 = 180
⇒ 5y + 60 = 180
⇒ 5y + 60 - 60 = 180 - 60
⇒ 5y = 120
⇒ 5y ÷ 5 = 120 ÷ 5
⇒ y = 24