The interior angles of a polygon are in ap

Asked by admin @ 10/08/2021 in Math viewed by 410 People

the angles of a polygon are in A.P. with common difference 5 degree if the smallest angle is 120 degree find the number of sides of the polygon

Answered by admin @ 10/08/2021

The angles of a polygon are in A.P. with common difference 5 degree if the smallest angle is 120 degree find the number of sides of the polygon

Let there be in n sides in the polygon.

sum of all n interior angles of polygon = (n – 2) * 180°

the angles are in A. P. with the smallest angle = 120°

common difference = 5°

∴ Sum of all interior angles of polygon

= n/2[2 * 120 + ( n – 1) * 5

n/2 [2 * 120 + (n – 1) * 5] = (n – 2) * 180

⇒ n/2 [5n + 235] = (n – 2 ) * 180

⇒ 5n2 + 235n = 360n – 720

⇒ 5n2 – 125n + 720 = 0 ⇒ n2 – 25n + 144 = 0

⇒ (n – 16 ) (n – 9) = 0 ⇒ n = 16, 9

Also if n = 16 then 16th angle = 120 + 15 * 5 = 195° > 180°

∴ not possible.

Hence n = 9.

What is the sum of interior angles of a polygon

Asked by admin @ 10/11/2021 in Mathematics viewed by 232 persons

The sum of the interior angles of s regular polygon is 3960, how many sides does it have? What is the measure of each interior angle? What is the measure …

If the interior angle of a polygon is 170

Asked by admin @ 23/08/2021 in Math viewed by 321 persons

Find the number of sides of a regular polygon if each interior angle is equal to 170 degree

The interior angle of a regular polygon is 156

Asked by admin @ 20/08/2021 in Math viewed by 258 persons

The interior angle of regular polygon is 156 degree. find the number of sides of the polygon

How to find sum of interior angles of a polygon

Asked by admin @ 27/11/2021 in Mathematics viewed by 312 persons

Explain how the formula for finding the sum of the interior angle measures of a polygon is derived. (Site 1)

How to find sum of interior angles in a polygon

Asked by admin @ 22/11/2021 in Mathematics viewed by 286 persons

Explain how the formula for finding the sum of the interior angle measures of a polygon is derived. (Site 1)

Measure of each interior angle of a regular polygon

Asked by admin @ 20/08/2021 in Math viewed by 346 persons

Find the measure of each interior angle of a regular pentagon and regular hexagon(using formula) .

Which type of polygon has 6 sides and 6 angles

Asked by admin @ 09/11/2021 in Mathematics viewed by 335 persons

A convex polygon has 6 sides what is the sum of its interior angles

What is the sum of all angles of a polygon

Asked by admin @ 05/11/2021 in Mathematics viewed by 293 persons

The sum of the interior angles of s regular polygon is 3960, how many sides does it have? What is the measure of each interior angle? What is the measure …

The angles of a quadrilateral are in ap

Asked by admin @ 25/08/2021 in Math viewed by 251 persons

The angles of a quadrilateral are in A.P.If the greatest angle is double of the smallest angle,find all the four angles.

The angles of a triangle are in ap

Asked by admin @ 25/08/2021 in Math viewed by 286 persons

The angles of a triangle are in AP. The greatest angle is twice the least. Find all the angles of the triangle. Most correct and fastest answer = Brainliest Answer …