1. Problem a: Find $x$ where vertical angles are equal and adjacent angles sum to 180°. 2. Use the rule: adjacent angles on a straight line sum to 180°. 3. Calculate $x$ using $x + 107 = 180$ so $x = 180 - 107 = 73$. 4. Problem b: Find $w$ where opposite angles are equal and adjacent angles sum to 180°. 5. Use $w + 121 = 180$ so $w = 59$. 6. Problem c: Find $y$ where opposite angles are equal and adjacent angles sum to 180°. 7. Use $119 + 61 = 180$ (check), then $y + y = 180$ so $2y = 180$ and $y = 90$. 8. Problem d: Find $d$ where vertical angles are equal and adjacent angles sum to 180°. 9. Use $d + 152 = 180$ so $d = 28$. 10. Problem f: Angles around a point sum to 360°, and adjacent angles on a straight line sum to 180°. 11. Use $5x + 100 + 45 = 180$ so $5x + 145 = 180$ and $5x = 35$ so $x = 7$. 12. Problem g: Sum of angles around a point is 360°. 13. Calculate $64 + 87 + 131 + 3f = 360$ so $282 + 3f = 360$ and $3f = 78$ so $f = 26$. 14. Problem h: Vertical angles equal and adjacent angles sum to 180°. 15. Use $180 + 103 = 283$ (not a straight line), but vertical angles imply $11e = 103$ so $e = \frac{103}{11} = 9.36$ approx. 16. Problem i: Angles around a point sum to 360°. 17. Use $2x + x + 6x = 360$ so $9x = 360$ and $x = 40$. Final answers: a) $x = 73$ b) $w = 59$ c) $y = 90$ d) $d = 28$ f) $x = 7$ g) $f = 26$ h) $e \approx 9.36$ i) $x = 40$