Given that the triangle is isosceles, then ∠A is congruent to ∠B
The addition of the three angles of a triangle is equal to 180°, then
∠A + ∠B + ∠C = 180°
∠A + ∠A + 132° = 180°
2∠A = 180° - 132°
∠A = 48°/2
∠A = 24°
and
∠B = 24°
Given that the triangle is isosceles, then side AC is congruent to side CB, that is,
AC = CB
2x + 15 = 4x - 5
15 + 5 = 4x - 2x
20 = 2x
20/2 = x
10 = x
Therefore, each side measure:
AC = 2x + 15
AC = 2*10 + 15
AC = 35
CB = 4x - 5
CB = 4*10 - 5
CB = 35
AB = 4x + 12
AB = 4*10 + 12
AB = 52
Finally, the perimeter of the triangle is
P = AC + CB + AB
P = 35 + 35 + 52
P = 122