Answer:
x = 7.5
y = 8.5
Explanation:
Linear Pair
Two adjacent angles that sum to 180° (two angles which when combined together form a straight line).
To find x, equate the sum of the two angles with the variable x to 180° and solve:
⇒ (16x - 18)° + (10x + 3)° = 180°
⇒ 16x - 18 + 10x + 3 = 180
⇒ 26x - 15 = 180
⇒ 26x = 195
⇒ x = 7.5
Vertical Angles Theorem
When two straight lines intersect, the opposite vertical angles are congruent.
Therefore:
⇒ (16x - 18)° = 12y°
Substitute the found value of x into the equation and solve for y:
⇒ 16x - 18 = 12y
⇒ 16(7.5) - 18 = 12y
⇒ 120 - 18 = 12y
⇒ 102 = 12y
⇒ y = 8.5