1. **State the problem:** We need to find the values of angles $x_1$ and $x_2$ in a geometric figure involving a circle and a triangle with given angles $130^\circ$, $80^\circ$, and $10^\circ$. 2. **Recall important rules:** - The sum of angles in a triangle is $180^\circ$. - Angles on a straight line sum to $180^\circ$. - The measure of an exterior angle of a triangle equals the sum of the two opposite interior angles. 3. **Find $x_1$:** - Given $x_1 = 25^\circ$ (from the problem statement). 4. **Find $x_2$:** - The angles on the straight horizontal line are $80^\circ$, $x_2$, and $10^\circ$. - Sum of these angles is $180^\circ$: $$80^\circ + x_2 + 10^\circ = 180^\circ$$ - Simplify: $$x_2 + 90^\circ = 180^\circ$$ - Subtract $90^\circ$ from both sides: $$x_2 = 180^\circ - 90^\circ$$ - Calculate: $$x_2 = 90^\circ$$ 5. **Final answers:** - $x_1 = 25^\circ$ - $x_2 = 90^\circ$