| I. Interior angle of a regular pentagon is three times the exterior angles of a regular decagon. |
| II. In a convex hexagon the sum of all interior angles is equal to twice the sum of its exterior angles formed by producing the sides In the same order. |
| III. The number of diagonals of a polygon of n sides\[=\frac{n(n-1)}{2}-n.\] |
A) I is true
B) I and III are true
C) II and III are true
D) All of these
Correct Answer: D
Solution :
I. Interior angle of regular pentagon \[=\text{ }180-\]exterior angle \[=180{}^\circ -72{}^\circ =108{}^\circ \] and exterior angle of decagon \[=\frac{360}{10}=36{}^\circ \] II. Sum of all interior angle \[\left( n-2 \right)\times 180{}^\circ =\left( 6-2 \right)\times 180{}^\circ =4\times 180=720{}^\circ \] Sum of all exterior angles \[=\text{ }4\times 90=360{}^\circ \] Clearly sum of interior angle \[=\text{ }2\text{ }\times \]sum of all exterior angles III. Clearly number of diagonal of a polygon of n side \[=\frac{n(n-1)}{2}-n\]
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