29. In an isosceles triangle, one of the base angles is \( 48^{\circ} \). Calculate the size of the vertex angle. Answer. \( \qquad \) (2.) 30. A plot of land has a perimeter of 210 me tres. If the length of the plot is 70 metres, what is the width? Answer. \( \qquad \) (2)

### Problem 29 **In an isosceles triangle, one of the base angles is \(48^{\circ}\). Calculate the size of the vertex angle.** **Solution:** 1. **Understanding the Triangle:** - An isosceles triangle has two equal sides and two equal base angles. - Given one base angle is \(48^{\circ}\), the other base angle is also \(48^{\circ}\). 2. **Sum of Angles in a Triangle:** \[ \text{Sum of angles} = 180^{\circ} \] 3. **Calculating the Vertex Angle:** \[ \text{Vertex angle} = 180^{\circ} - (\text{Base angle}_1 + \text{Base angle}_2) = 180^{\circ} - (48^{\circ} + 48^{\circ}) = 180^{\circ} - 96^{\circ} = 84^{\circ} \] **Answer:** The vertex angle measures \(84^{\circ}\). --- ### Problem 30 **A plot of land has a perimeter of 210 metres. If the length of the plot is 70 metres, what is the width?** **Solution:** 1. **Assumption:** - The plot is rectangular. (If the shape is different, additional information is required.) 2. **Formula for Perimeter of a Rectangle:** \[ P = 2 \times (\text{Length} + \text{Width}) \] 3. **Plugging in the Known Values:** \[ 210 = 2 \times (70 + \text{Width}) \] \[ 105 = 70 + \text{Width} \] \[ \text{Width} = 105 - 70 = 35 \text{ metres} \] **Answer:** The width of the plot is \(35\) metres.