Question

in a polygon there are 5 right angle and the remaining angles are equal to 195° each find the number of sides in the polygon​

Answer 1

Topic

Understanding Polygons

Given

In a polygon,

• There are 5 Right angles.

• Remaining angles = 195°

To Find

Number of sides in given polygon.

Formula to be Used

Sum of all angles in a polygon is given by,

( n - 2 ) × 180°

where,

n = Number of Sides in Polygon

Solution

Let 'n' be the total number of sides in given polygon.

A polygon has same number of angles as of sides.

It is given that 5 angles are right angles and remaining angles are 195°.

So, ( n - 5 ) angles are of 195°; as total sides = n.

Now,

Sum of all angles inside the polygon will be

5 × ( 90° ) + ( n - 5 ) × 195°

450° + 195n - 975°

195n - 525°

It is equal to the formula mentioned above.

195n - 525 = ( n - 2 ) × 180°

195n - 525 = 180n - 360°

195n - 180n = 525 - 360

15n = 165

n = 165 / 15

n = 11

So, value of n = 11.

Answer

The given polygon has 11 sides and it is a hendecagon.