Answer:
x = 8
Explanation:
Formula for sum of interior angles is 180(n - 2)
For a 5 sided polygon the sum is;
180(5 - 2) =540°
The supplement of ∡ 59° = 180° - 59° = 121°
The supplement of ∡ 77° = 180° - 77° = 103°
The supplement of ∡ 66° = 180° - 66° = 114°
The supplement of ∡ 62° = 180° - 62° = 118°
The sum of the polygon is:
121° + 103° + 114° + 118° + (180 - 12x)° = 540°
456° + (180 - 2x)° = 540°
(180 -12x)° = 540° - 456° = 84°
12x = 180° - 84° = 96°
x = 96/12 = 8