Question

In a polygon there are 5 right angles and the remaining angles are equal to 195o each. Find the number of sides in the polygon.

Answer 1

★Answer :-

Therefore ,

• There are 11 sides in the polygon .

★Step-by-Step-Explanation :-

★Let ::

• Let  ' n ' be the no. of sides .

★Step for solving it :-

Here , given to us is that a polygon is having 5 right angles and the other remaining angles are equal to 195° . So, find how many sides are there . So, we know that .

$\rm Sum\;of\;interior \;angles \;of\; a \;polygon=(n-2)\times180^\circ$

Now , as we assumed n as no. of sides . And , there are 5 right angle . So, Formula becomes,

$\rm 5\times90^\circ+(n-5)\times195^\circ$

★Hence,

Final equation is :-

$\rm (n-2)\times180^\circ=450^\circ+(n-5)\times195^\circ$

So, let's solve ::

★Solution :

$\rm (n-2)\times180^\circ=450^\circ+(n-5)\times195^\circ$

Multiplying 180 with n and -2 and in R.H.S. also multiplying 195 with n and  -5

$\rm ::\implies180n-360^\circ=450^\circ+195n-975^\circ$

Bringing n to L.H.S. and No. to R.H.S.

$\rm::\implies 195n-180n=525^\circ-360^\circ$

Now , subtracting

$\rm::\implies15n=165^\circ$

n will remain this side but 15 will go and being divided

$\rm::\implies n=\dfrac{165^\circ}{15^\circ}$

$\rm::\implies n = 11$

$\rm\underline {\bf n=11 \;sides}$

Hence , the no. of sides the given polygon is having is 11 sides .

★Additional Information !!

• Polygon having three sides ➢Triangle
• Polygon having four sides ➢Quadrilateral
• Polygon having five sides  ➢Pentagon
• Polygon having six sides  ➢ Hexagon
• Polygon having seven sides ➢Heptagon
• Polygon having eight sides  ➢Octagon
• Polygon having nine sides  ➢Nonagon
• Polygon having ten sides  ➢Decagon

1. Sum of interior angles of a polygon with n sides = 180° (n-2) .
2. Measure of exterior angles of a regular n-sided polygon = 360° / n