1.

Fill in the blanks.i. Each interior angles of a regular octagon is (......)°.ii. The sum of all interior angle of a regular hexagon is (......)°.iii. Each exterior angle of a regular polygon is 60°. This polygon is a ...... . iv. Each interior angle of a regular polygon is 108°. This polygon is a ...... . v. A pentagon has ...... diagonals.

Answer»

i. 135°

Exterior Angle = \(\frac{360}{8}\) [n represents no of sides of polygon]

= 45°

Interior Angle + Exterior Angle = 180o 

Interior Angle = 180 – 45 = 135° 

ii. 720° 

Sum of Interior Angle = (n - 2)× 180° 

= (6 - 2) × 180 ° 

= 720°

iii. Hexagon

Exterior Angle = \(\frac{360}{n}\)

60 = \(\frac{360}{n}\)

N = \(\frac{360}{60}\)

= 6

No. of Sides is 6. 

So, it is a hexagon. 

iv. Pentagon 

Interior Angle = 108° 

Exterior Angle = 180° - 108° = 72°

No. of Sides = \(\frac{360}{72}\)

= 5

So, it is a pentagon. 

v. 5

No. of diagonals = \(\frac{n(n\,-\,3)}{2}\) [n is No. of Sides]

\(\frac{5\times(5\,-\,3)}{2}\)

= 5



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