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)

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### 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 $$84^{\circ}$$.

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### 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.
**Problem 29:** - In an isosceles triangle, one base angle is $$48^{\circ}$$. - The vertex angle is $$84^{\circ}$$. **Problem 30:** - A rectangular plot has a perimeter of 210 metres and a length of 70 metres. - The width of the plot is $$35$$ metres.

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)

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