1. **State the problem:** We need to find the values of angles $a$, $b$, and $c$ given the angles $49^\circ$ and $83^\circ$ in a figure with intersecting lines. 2. **Use the properties of intersecting lines:** When two lines intersect, opposite (vertical) angles are equal. 3. **Find $a$:** Angle $a$ is adjacent to $49^\circ$ and together they form a straight line, so they are supplementary. $$a + 49 = 180$$ Solve for $a$: $$a = 180 - 49 = 131$$ 4. **Find $c$:** Angle $c$ is vertically opposite to $49^\circ$, so $$c = 49$$ 5. **Find $b$:** Angle $b$ is vertically opposite to $83^\circ$, so $$b = 83$$ **Final answers:** $$a = 131^\circ, \quad b = 83^\circ, \quad c = 49^\circ$$