Applying the exterior angle theorem, the value of x in the diagram given is: x = 23.
Given:
- Exterior angle = 113 degrees
- Two interior angles opposite to the exterior angle are: x and 90 degrees respectively.
Based on the exterior angle theorem of a triangle, we will have the following:
x + 90 = 113 (exterior angle theorem)
- Subtract 90 from each side
x + 90 - 90 = 113 - 90
x = 23
Thus, applying the exterior angle theorem, the value of x in the diagram given is: x = 23.
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