Question

The angle of a hexagon are in
arthmetic
aequence. prove that is
amallest sangle is always greather
60
than​

Answer 1

CORRECT QUESTION:

The angle of a hexagon are in arithmetic

sequence. prove that the smallest angle is always greater than 60°

GIVEN:

The angle of a hexagon are in arithmetic

sequence

TO PROVE:

The smallest angle is always greater than 60°.

FORMULAE:

SUM OF INTERIOR ANGLES OF A POLYGON = ( n - 2) × 180°

PROOF:

Number of sides in a hexagon = 6

Substitute n = 6 in ( n - 2) × 180°

Sum of interior angles of a hexagon = (6 - 2) × 180°

Sum of interior angles of a hexagon = 4 × 180°

Sum of interior angles of a hexagon = 720°

a + a + d + a + 2d + a + 3d + a + 4d + a + 5d = 720°

6a + 15d = 720°

Divide by 3 on both sides

2a + 5d = 240°

a + 5d = 240° - a

Substitute a = 60° on right side

a + 5d = 240° - 60°

a + 5d = 180°

180° means it is a straight line which cannot be possible as the largest possible angle is always less than 179°, the smallest possible angle should be always greater than 60°.

HENCE PROVED.