1. **Problem b:** Find $x$ given angles $95^\circ$ and $125^\circ$ around a point. 2. **Step 1:** Recall that the sum of angles around a point is $360^\circ$. 3. **Step 2:** Use the formula: $$x + 95^\circ + 125^\circ = 360^\circ$$ 4. **Step 3:** Simplify the known angles: $$95^\circ + 125^\circ = 220^\circ$$ 5. **Step 4:** Solve for $x$: $$x = 360^\circ - 220^\circ = 140^\circ$$ --- 1. **Problem c:** Find $x$ in a circle with an inscribed angle $33.5^\circ$ and angle $x$. 2. **Step 1:** Recall that the measure of an inscribed angle is half the measure of its intercepted arc. 3. **Step 2:** If $x$ is the angle subtending the same arc as $33.5^\circ$, then: $$x = 2 \times 33.5^\circ = 67^\circ$$ --- 1. **Problem d:** Find $x$ and $y$ in a triangle with angles $35^\circ$, $35^\circ$, and $y$. 2. **Step 1:** Given $x = 35^\circ$ as it corresponds to the other $35^\circ$. 3. **Step 2:** Use the triangle angle sum property: $$35^\circ + 35^\circ + y = 180^\circ$$ 4. **Step 3:** Solve for $y$: $$y = 180^\circ - 70^\circ = 110^\circ$$ **Final answers:** - b) $x = 140^\circ$ - c) $x = 67^\circ$ - d) $x = 35^\circ$, $y = 110^\circ$