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 = [tex]\frac{360}{5}[/tex] = 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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