The value of x in the triangle is 90 degrees.
How to find the angle of a triangle?
The exterior angle of a triangle is equal to the sum of the two opposite interior angles (remote interior angles).
This is also known as the Exterior Angle theorem.
The triangle is an isosceles triangle. Therefore, the base angles are equal.
Hence,
180 - 135 = 45°(sum of angles on a straight line)
Therefore, using external triangle theorem,
45 + x = 135
subtract 45 from both sides of the equation
45 - 45 + x = 135 - 45
x = 90 degrees.
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