A star is drawn on the inside of a regular pentagon, as shown below.
What is the size of the angle marked `x`? (3 marks)
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`text(Consider the triangle)\ ABC\ \ text(in the pentagon:)`
STRATEGY: The internal angle sum is 3 × 180 = 540 (since 3 triangles can be drawn internally from one point).
`text(Total degrees in a pentagon)`
`= 3 xx 180`
`= 540^@`
`text{Internal angle}\ =540/5 = 108^@\ \ \text{(regular pentagon)}`
`DeltaABC\ text(is isosceles)`
| `:. x + x + 108` | `= 180` |
| `2x` | `= 72` |
| `x` | `= 36^@` |