The diagram shows a regular pentagon with centre O.

Work out the size of angle x.

The angle between diagonal of a pentagon is 72°.

The size of angle x is 54°.

Let 'O' is a complete angle

∴ ∠O = 360°

Angle between diagonals = = 72°

All the diagonals of a pentagon are equal so, their opposite angles of equal diagonals are also equal.

The sum of all interior angles of triangle is 180°

x + x + 72° = 180°

2x = 180°  - 72°

2x = 108°

x = 54°

Therefore, the size of angle x is 54°.

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54

Step-by-step explanation:

Each vertex of the pentagon has an angle of 108 degrees. So, x = 108/2 = 54

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step-by-step explanation: