For this case we have that by definition, the sum of the internal angles of a triangle is 180 degrees. So, we have:
[tex]69+ (9y-3) + (5x + 2) = 180[/tex]
According to the figure, we have an isosceles triangle because the sides AB and BC are equal. Therefore it is fulfilled that:
[tex]69 = 9y-3[/tex]
We clear the value of the variable "y":
[tex]69 + 3 = 9y\\72 = 9y\\y = \frac {72} {9}\\y = 8[/tex]
Therefore we have:
[tex]69+ (9 (8) -3) + (5x + 2) = 180\\69+ (72-3) + (5x + 2) = 180\\69 + 69 + (5x + 2) = 180\\69 + 69 + 5x + 2 = 180[/tex]
We add similar terms:
[tex]140 + 5x = 180\\5x = 180-140\\5x = 40\\x = \frac {40} {5}\\x = 8[/tex]
Answer:
[tex]x=8[/tex]
