Find the missing angle in each irregular polygon using the sum of interior angles.

To find the missing angle in each irregular polygon, I need to use the formula for the sum of interior angles:

Sum of interior angles = (n - 2) × 180°, where n is the number of sides.

Then I subtract all the known angles from this total to find x.

Let me work through each one carefully:

(a) This is a quadrilateral (4 sides).
- Sum = (4 - 2) × 180° = 360°
- Known angles: 70°, 88°, 45°
- x = 360° - 70° - 88° - 45° = 360° - 203° = 157°

(b) This is a pentagon (5 sides).
- Sum = (5 - 2) × 180° = 540°
- Known angles: 84°, 153°, 131°, 105°
- x = 540° - 84° - 153° - 131° - 105° = 540° - 473° = 67°

(c) This is a hexagon (6 sides).
- Sum = (6 - 2) × 180° = 720°
- Known angles: 120°, 130°, 100°, 110°, 135°
- x = 720° - 120° - 130° - 100° - 110° - 135° = 720° - 595° = 125°

(d) This is a pentagon (5 sides) with three right angles (90° each).
- Sum = (5 - 2) × 180° = 540°
- Known angles: 90°, 90°, 90°, 143°
- x = 540° - 90° - 90° - 90° - 143° = 540° - 413° = 127°

(e) This is a heptagon (7 sides).
- Sum = (7 - 2) × 180° = 900°
- Known angles: 96°, 105°, 161°, 123°, 155°, 114°
- x = 900° - 96° - 105° - 161° - 123° - 155° - 114° = 900° - 854° = 46°

(f) This is a hexagon (6 sides) with two right angles (90° each).
- Sum = (6 - 2) × 180° = 720°
- Known angles: 150°, 127°, 202°, 40°, and two 90° angles
- x = 720° - 150° - 127° - 202° - 40° - 90° - 90° = 720° - 699° = 21°

Let me verify my calculations using code to be sure.