Angles Polygons 9E4783

1. **Problem 3: Find the value of $x$ given two parallel lines and angles $145^\circ$ and $41^\circ$.** 2. When two lines are parallel, alternate interior angles or corresponding angles are equal. 3. The angles on a straight line add up to $180^\circ$. 4. Since $145^\circ$ and $x$ are on a straight line, we have: $$145^\circ + x = 180^\circ$$ 5. Solve for $x$: $$x = 180^\circ - 145^\circ = 35^\circ$$ 6. **Answer for problem 3:** $x = 35^\circ$ --- 7. **Problem 4a: Find the sum of the interior angles of a nonagon (9 sides).** 8. The formula for the sum of interior angles of a polygon with $n$ sides is: $$\text{Sum} = (n - 2) \times 180^\circ$$ 9. Substitute $n=9$: $$\text{Sum} = (9 - 2) \times 180^\circ = 7 \times 180^\circ = 1260^\circ$$ 10. **Answer for 4a:** The sum of interior angles is $1260^\circ$ --- 11. **Problem 4b: Find the interior angle of a regular nonagon.** 12. A regular polygon has all interior angles equal. 13. Each interior angle is: $$\frac{\text{Sum of interior angles}}{n} = \frac{1260^\circ}{9} = 140^\circ$$ 14. **Answer for 4b:** Each interior angle is $140^\circ$ --- 15. **Problem 5: Find the number of sides of a polygon with interior angles sum $900^\circ$.** 16. Use the formula: $$900^\circ = (n - 2) \times 180^\circ$$ 17. Divide both sides by $180^\circ$: $$\frac{900^\circ}{180^\circ} = n - 2$$ $$5 = n - 2$$ 18. Solve for $n$: $$n = 5 + 2 = 7$$ 19. **Answer for problem 5:** The polygon has $7$ sides.