Answer:
x = 36
y = 34
Step-by-step explanation:
✔️Sum of the interior angles of an n-sided polygon = (n - 2) × 180
Thus, the figure given is a hexagon with 6 sides.
Therefore, the sum of its interior angles = (6 - 2) × 180
= 4 × 180 = 720.
This means:
(5x) + (4x + 2) + (5x + 5) + (2x - 2) + (3x + 5) + (x - 10) = 720
Solve for x
5x + 4x + 2 + 5x + 5 + 2x - 2 + 3x + 5 + x - 10 = 720
Add like terms
20x = 720
Divide both sides by 20
x = 36
✔️(2y - 1) + (3x + 5) = 180 (angles on a straight line)
Plug in the value of x
2y - 1 + 3(36) + 5 = 180
2y - 1 + 108 + 5 = 180
Add like terms
2y + 112 = 180
Subtract 118 from each side
2y = 180 - 112
2y = 68
Divide both sides by 2
y = 68/2
y = 34
