1. **State the problem:** We need to find the unknown angles $x$, $y$, and $w$ in the given triangles. 2. **Given information:** - Large triangle has angles $61^\circ$ and $95^\circ$. - First smaller triangle has angles $38^\circ$, $x^\circ$, and $y^\circ$. - Second smaller triangle has angles $121^\circ$ and $w^\circ$. - $y = 24^\circ$ is given. 3. **Use the triangle angle sum rule:** The sum of angles in any triangle is $180^\circ$. 4. **Find the third angle in the large triangle:** $$ \text{Third angle} = 180^\circ - 61^\circ - 95^\circ = 24^\circ $$ 5. **Find $x$ in the first smaller triangle:** Sum of angles = $180^\circ$ $$ x + 38^\circ + y = 180^\circ$$ Substitute $y = 24^\circ$: $$ x + 38^\circ + 24^\circ = 180^\circ$$ $$ x + 62^\circ = 180^\circ$$ $$ x = 180^\circ - 62^\circ = 118^\circ $$ 6. **Find $w$ in the second smaller triangle:** Sum of angles = $180^\circ$ $$ 121^\circ + w + \text{third angle} = 180^\circ $$ Since the second smaller triangle shares the side with the large triangle, the third angle here is the same $24^\circ$ found in step 4. $$ 121^\circ + w + 24^\circ = 180^\circ $$ $$ 145^\circ + w = 180^\circ $$ $$ w = 180^\circ - 145^\circ = 35^\circ $$ **Final answers:** $$x = 118^\circ, \quad y = 24^\circ, \quad w = 35^\circ$$