1. **State the problem:** We are given a triangle with one angle measuring 75°, another angle unknown (labeled "?"), and an exterior angle adjacent to the unknown angle measuring 142°. 2. **Recall the exterior angle theorem:** The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles. 3. **Set up the equation:** Let the unknown angle be $x$. The exterior angle adjacent to $x$ is 142°, so $$142 = 75 + x$$ 4. **Solve for $x$:** $$x = 142 - 75$$ $$x = 67$$ 5. **Answer:** The unknown angle measure is $67^\circ$.