Answer x = 8
Step by step
We know the three interior angles of a triangle will always have a sum of 180°.
Here we know triangle DEF is an Isosceles Triangle. Two sides are congruent to each other noted by the tick marks.
The two angles opposite to the equal sides are congruent to each other.
So we know:
D = 11x - 18
F= 11x - 18
E = 40
Total to equal 180, so our equation is
2(11x - 18) + 40 = 180
Multiply
22x - 36 + 40 = 180
Simplify
22x + 4 = 180
Subtract 4 from both sides to isolate variable
22x + 4 - 4 = 180 - 4
Simplify
22x = 176
Divide both sides by 22 to solve for x
22/22 x = 176/22
x = 8
Now solve your unknown angles
D = 11x - 18
D = 11(8) - 18
D = 88 - 18
D = 70
F= 11x - 18
F = 11(8) - 18
F = 88 - 18
F = 70
Now add all three angles
70 + 70 + 40 = 180
Problem solved!