1. **State the problem:** We are given six angles around a point: $(g-86)^\circ$, $(6f)^\circ$, $45^\circ$, $15^\circ$, $(e-27)^\circ$, and $d^\circ$. We need to find the value of $e$. 2. **Important rule:** The sum of all angles around a point is $360^\circ$. 3. **Set up the equation:** $$ (g-86) + (6f) + 45 + 15 + (e-27) + d = 360 $$ 4. **Simplify the constants:** $$ 45 + 15 - 27 = 33 $$ 5. **Rewrite the equation:** $$ (g - 86) + (6f) + (e - 27) + d + 60 = 360 $$ 6. **Combine constants:** $$ (g - 86) + (6f) + (e - 27) + d + 60 = 360 $$ $$ g + 6f + e + d - 86 - 27 + 60 = 360 $$ $$ g + 6f + e + d - 53 = 360 $$ 7. **Isolate $e$:** $$ e = 360 + 53 - g - 6f - d $$ $$ e = 413 - g - 6f - d $$ **Final answer:** $$ e = 413 - g - 6f - d $$ Without values for $g$, $f$, and $d$, this is the expression for $e$.