1. The problem is to find the value of angle $x$ in a triangle where the angles given are $65^\circ$ and $20^\circ$, and the triangle has a right angle. 2. Recall that the sum of the interior angles in any triangle is always $180^\circ$. 3. Since the triangle has a right angle, one angle is $90^\circ$. 4. The sum of the three angles is: $$x + 65^\circ + 20^\circ = 180^\circ$$ 5. Combine the known angles: $$65^\circ + 20^\circ = 85^\circ$$ 6. Substitute back: $$x + 85^\circ = 180^\circ$$ 7. Solve for $x$ by subtracting $85^\circ$ from both sides: $$x = 180^\circ - 85^\circ$$ 8. Calculate the result: $$x = 95^\circ$$ 9. Therefore, the value of $x$ is $95^\circ$.