1. **Problem statement:** Calculate angle $\phi$ in degrees and minutes. 2. **Understanding the problem:** Angle $\phi$ is part of the polygon's interior angles. We need to find its value in degrees and minutes without converting to decimal degrees. 3. **Given data:** The problem provides several angles around the polygon, but for $\phi$, we use the relationship between adjacent angles or supplementary angles if applicable. 4. **Formula and rules:** Angles on a straight line sum to $180^\circ$. If $\phi$ is supplementary to a given angle, then: $$\phi = 180^\circ - \text{given angle}$$ 5. **Calculation:** From the problem context, $\phi$ is supplementary to $44^\circ 27'$. Calculate $\phi$: $$\phi = 180^\circ 0' - 44^\circ 27'$$ Subtract minutes: $$0' - 27' = \text{cannot subtract, borrow }1^\circ = 60'$$ So: $$\phi = 179^\circ 60' - 44^\circ 27'$$ Subtract minutes: $$60' - 27' = 33'$$ Subtract degrees: $$179^\circ - 44^\circ = 135^\circ$$ Therefore: $$\phi = 135^\circ 33'$$ 6. **Answer:** $\phi = 135^\circ 33'$