Answer:
x = 15
y = 50
Explanation:
Linear Pair
Two adjacent angles that sum to 180° (two angles which when combined together form a straight line).
The angles (8x + 10)° and y° form a linear pair.
Therefore, equate the sum of these angles to 180° and isolate y:
⇒ (8x + 10)° + y° = 180°
⇒ 8x + 10 + y = 180
⇒ 8x + 10 + y - 10 = 180 - 10
⇒ 8x + y = 170
⇒ 8x + y - 8x = 170 - 8x
⇒ y = 170 - 8x
Corresponding Angles Postulate
When a straight line intersects two parallel straight lines, the resulting corresponding angles are congruent.
The angles y° and (3x + 5)° are corresponding angles and are therefore congruent:
⇒ y° = (3x + 5)°
⇒ y = 3x + 5
Substitute the second equation for y into the first equation for y and solve for x:
⇒ 3x + 5 = 170 - 8x
⇒ 3x + 5 + 8x = 170 - 8x + 8x
⇒ 11x + 5 = 170
⇒ 11x + 5 - 5 = 170 - 5
⇒ 11x = 165
⇒ 11x ÷ 11 = 165 ÷ 11
⇒ x = 15
Substitute the found value of x into one of the expression for y and solve for y:
⇒ y = 170 - 8x
⇒ y = 170 - 8(15)
⇒ y = 170 - 120
⇒ y = 50
Final solution: