1. **Problem statement:** Find the value of the angle marked $y$ in the given quadrilateral. 2. **Given angles:** - Top center angle: $70^\circ$ - Right upper angle: $44^\circ$ - Bottom center angle: $48^\circ$ - Left lower angle: $77^\circ$ - Unknown angles: $x$ and $y$ 3. **Important rule:** The sum of interior angles in any quadrilateral is $360^\circ$. 4. **Step 1:** Sum all known angles and unknown angles: $$70 + 44 + 48 + 77 + x + y = 360$$ 5. **Step 2:** Calculate the sum of known angles: $$70 + 44 + 48 + 77 = 239$$ 6. **Step 3:** Substitute back: $$239 + x + y = 360$$ 7. **Step 4:** Simplify to find relation between $x$ and $y$: $$x + y = 360 - 239 = 121$$ 8. **Step 5:** Use the kite property: in a kite, the angles between unequal sides are equal. Given the kite shape, angles $x$ and $y$ are equal. 9. **Step 6:** Set $x = y$ and solve: $$x + y = 121 \Rightarrow y + y = 121 \Rightarrow 2y = 121$$ 10. **Step 7:** Divide both sides by 2: $$\cancel{2}y = \cancel{2} \times 60.5$$ 11. **Step 8:** Simplify: $$y = 60.5^\circ$$ **Final answer:** $$\boxed{y = 60.5^\circ}$$