Question

The interior angles of a hexagon are x°,(x+20)°,(x+40)°,(x+60)°,

(x+80)° and (x-20)°.Find the smallest angle of the hexagon.​

Answer 1

Answer:

The interior angles of a hexagon are x, x +100

, x+200

, x+300

, x+400 and x+500

.

Find x

Answer 2

Answer:

The smallest of all the angles is 70°

Step-by-step explanation:

Hexagon:

• A polygon with six sides is called a hexagon.

• A polygon's internal angle is the angle between its two adjacent sides.

There are two techniques to determine the sum of a hexagon's internal angles:

• Dividing the hexagon into triangles.

• Interior angle sum formula

We use here Interior angle sum formula:

Given interior angles of a hexagon are

  x°, (x+20)°, (x+40)°, (x+60)°, (x+80)° and (x-20)°

 Sum of the interior angles of hexagon = 720°

As per the given data

       x+x+20+x+40+x+60+x+80+x-20 = 720

                   6x+180 = 720

                    6x = 720-180

                    6x = 540

                      x = 540/6

                      x = 90°

      now substitute x = 90° in the angles given

            x = 90°

      x+20 = 90+20 = 110°

      x+40 = 90+40 = 130°

      x+60 = 90+60 = 150°

      x+80 = 90+80 = 170°

      x-20 = 90-20 = 70°

        Hence, the smallest of all the angles is 70°.

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