Calculate the angle heta formed by the two lines defined by points A(0, 5), C(4, 0) and A(0, 5), B(-3, 0).

Here are the solutions for the requested problems from the image.

1.a) Calculate the angle $\theta$ formed by the two lines.

Step 1: Identify the coordinates of the points on the lines.
Line 1 passes through A(0, 5) and C(4, 0).
Line 2 passes through A(0, 5) and B(-3, 0).

Step 2: Calculate the gradient of Line 1 ($m_1$).

$$m_1 = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 5}{4 - 0} = \frac{-5}{4}$$

Step 3: Calculate the gradient of Line 2 ($m_2$).

$$m_2 = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 5}{-3 - 0} = \frac{-5}{-3} = \frac{5}{3}$$

Step 4: Use the formula for the angle $\theta$ between two lines.

$$\tan \theta = \left| \frac{m_1 - m_2}{1 + m_1 m_2} \right|$$ $$\tan \theta = \left| \frac{-\frac{5}{4} - \frac{5}{3}}{1 + \left(-\frac{5}{4}\right)\left(\frac{5}{3}\right)} \right|$$ $$\tan \theta = \left| \frac{\frac{-15 - 20}{12}}{1 - \frac{25}{12}} \right|$$ $$\tan \theta = \left| \frac{\frac{-35}{12}}{\frac{12 - 25}{12}} \right|$$ $$\tan \theta = \left| \frac{\frac{-35}{12}}{\frac{-13}{12}} \right|$$ $$\tan \theta = \left| \frac{-35}{-13} \right| = \frac{35}{13}$$

Step 5: Calculate $\theta$ and round to two decimal places.

$$\theta = \arctan\left(\frac{35}{13}\right)$$ $$\theta \approx 69.593^\circ$$ $$\theta \approx \boxed{\text{69.59}^\circ}$$

1.c) Calculate the angle $\theta$ formed by the two lines.

Step 1: Identify the coordinates of the points on the lines.
Line 1 passes through A(-2, 1) and B(1, 5).
Line 2 passes through C(0, 4) and D(3, 2).

Step 2: Calculate the gradient of Line 1 ($m_1$).

$$m_1 = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5 - 1}{1 - (-2)} = \frac{4}{3}$$

Step 3: Calculate the gradient of Line 2 ($m_2$).

$$m_2 = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 4}{3 - 0} = \frac{-2}{3}$$

Step 4: Use the formula for the angle $\theta$ between two lines.

$$\tan \theta = \left| \frac{m_1 - m_2}{1 + m_1 m_2} \right|$$ $$$$