The value of x = 40°
Step-by-step explanation:
To solve for x, we will use an illustration:
When two lines intersect, the angles opposite each other are vertical angles. Vertical angles are equal.
The angles marked in magenta are equal.
The angle by the right in magenta colour will also be 52°.
The sum of angles in a triangle = 180°
x° + 52° + 88° = 180°
x + 140 = 180
subtract 140 from both sides:
x + 140 - 140 = 180 - 140
x = 40°