- Determine the value of \(a^{\circ}\), giving reasons for your answer. (2 marks)
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- Determine the value of \(b^{\circ}\), giving reasons for your answer. (2 marks)
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Show Answers Only
a.
\(\text{All radii are equal (see diagram).}\)
\(\text{Isosceles triangle}\ \ \Rightarrow\ \ \text{angles opposite equal sides are equal}\)
\(a^{\circ} = 180-(2 \times 60)=60^{\circ}\ \ \text{(angle sum of triangle)} \)
b. \(c^{\circ} = 180-60=120^{\circ}\ \ \text{(180° in straight line)} \)
| \(120^{\circ}\) | \(=85\ \ \text{(external angle = sum of interior opposite angles)} \) | |
| \(a^{\circ}\) | \(= \dfrac{85}{2}\) | |
| \(=42.5^{\circ}\) |
Show Worked Solution
a.
\(\text{All radii are equal (see diagram).}\)
\(\text{Isosceles triangle}\ \ \Rightarrow\ \ \text{angles opposite equal sides are equal}\)
\(a^{\circ} = 180-(2 \times 60)=60^{\circ}\ \ \text{(angle sum of triangle)} \)
b. \(c^{\circ} = 180-60=120^{\circ}\ \ \text{(180° in straight line)} \)
| \(120^{\circ}\) | \(=85\ \ \text{(external angle = sum of interior opposite angles)} \) | |
| \(a^{\circ}\) | \(= \dfrac{85}{2}\) | |
| \(=42.5^{\circ}\) |