In die diagram sly dat hoeke van vierhoek CDEF mekaar by T - NSC Mathematics - Question 9 - 2019 - Paper 2

To prove the equality of angles EFĎ and ĒCD, we can use the following reasoning based on the properties of cyclic quadrilaterals:

1. Using the properties of cyclic quadrilaterals:

   • In a cyclic quadrilateral, opposite angles are supplementary, meaning that the sum of the angles equals 180 degrees.

2. Identify the relevant angles:

   • Given that points E, F, C, and D are on the circumference of a circle, we focus on angles EFĎ and ĒCD.

3. Applying the angle properties:

   • From angle properties, we can say: $ext{Angle EFĎ} + ext{Angle ĒCD} = 180°$
   • If we denote angle EFĎ as x and angle ĒCD as y, we can express this as: $x + y = 180°$

4. Substituting known values:

   • Based on the given lengths for EF, DC, ET, and others, we can infer that the angles formed by these segments maintain the cyclic property and thereby yield: $ext{Angle EFĎ} = ext{Angle ĒCD}$
   • This indicates that the two angles are equal in measure.

5. Conclusion:

   • Thus, we conclude that EFĎ indeed equals ĒCD as required: $ext{EFĎ} = ext{ĒCD}$