1. The problem asks to find the size of angle $x$ given two adjacent angles on a straight line: $50^\circ$ and $35^\circ$. 2. Important rule: Angles on a straight line add up to $180^\circ$. 3. Using the formula for angles on a straight line: $$50^\circ + x + 35^\circ = 180^\circ$$ 4. Combine the known angles: $$50^\circ + 35^\circ = 85^\circ$$ 5. Substitute back: $$85^\circ + x = 180^\circ$$ 6. Solve for $x$ by subtracting $85^\circ$ from both sides: $$x = 180^\circ - 85^\circ$$ 7. Calculate the difference: $$x = 95^\circ$$ 8. Therefore, the size of angle $x$ is $95^\circ$.