Question

1)The angles of a pentagon are in arithmetic sequence. Prove
that the smallest angle is greater than 360?​

Answer 1

Step-by-step explanation:

Answer:

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Step-by-step explanation:

Sum of all angles of a regular polygon with n sides = (n-2) × 180

Let a,a + d,a + 2d,a + 3d,a + 4d are 5 terms of an AP.

Sum of all angles = 5a + 10d = (5-2) × 180 = 540

∴ a + 2d = 108

The minimum angle will be obtained when a = d.

a + 2a = 3a = 108

∴ a = 36 is the minimum angle.

Answer 2

Step-by-step explanation:

no.of triangles of regular polygon having no.of sides are..5

sum of iterior angles of a triangle is 180°

then the sequence of sum of interior angles

=180,180×2,180×3,180×5.......=180,360,540,900

sum of exterior angles of any geometric structure having any numbers of side is always360°

sum of exterior angles=360,360........

one interior angle=

360/3,360/4,360/5............=120 ,90,72........