1. **Stating the problem:** (a) Find the degrees in a right angle and in 2 right angles. (b) Complete the table showing the sum of interior angles of polygons in terms of right angles. (c) Show the linear relationship between the number of sides and the sum of interior angles in right angles. 2. **Important formulas and rules:** - A right angle is defined as 90 degrees. - The sum of interior angles of an n-sided polygon is given by the formula: $$\text{Sum of angles} = (n-2) \times 180^\circ$$ - Since 1 right angle = 90 degrees, sum in right angles is: $$\frac{(n-2) \times 180}{90} = 2(n-2)$$ 3. **Part (a) solution:** - Degrees in a right angle = 90° - Degrees in 2 right angles = $2 \times 90 = 180^\circ$ 4. **Part (b) complete the table:** | Polygon | Number of sides (n) | Sum of angles in right angles | |--------------|---------------------|-------------------------------| | Triangle | 3 | $2(3-2) = 2$ | | Quadrilateral| 4 | $2(4-2) = 4$ | | Pentagon | 5 | $2(5-2) = 6$ | | Hexagon | 6 | $2(6-2) = 8$ | | Heptagon | 7 | $2(7-2) = 10$ | | Octagon | 8 | $2(8-2) = 12$ | 5. **Part (c) show linear relationship:** - Let $S$ be the sum of interior angles in right angles, and $n$ the number of sides. - From the formula: $$S = 2(n-2) = 2n - 4$$ - This is a linear equation in $n$ with slope 2 and intercept $-4$. - This means the sum of interior angles in right angles increases linearly as the number of sides increases. **Final answers:** - (a) 90 degrees in a right angle, 180 degrees in 2 right angles. - (b) Table completed as above. - (c) Linear relationship: $$S = 2n - 4$$ where $S$ is sum in right angles and $n$ is number of sides.