Question

The measures of the angles of a hexagon are in the extended ratio 4 : 5 : 5 : 8 : 9 : 9. What is the measure of the smallest angle in the hexagon?

Answer 1

`72^(\circ)` is the measure of the smallest angle in the hexagon.

Explanation:

As, we know that the sum of all the angles is 720 degrees.

Given: The measures of the angles of the hexagon are in the extended ratio 4 : 5 : 5 : 8 : 9 : 9.

Let x be the number used to simplify the size of each angle.

Sum of all the measure angles is 720 degrees

⇒
`4x+5x+5x+8x+9x+9x = 720^(\circ)`

Combine like terms;

`40x = 720^(\circ)`

Divide both sides by 40 we get;

`x = (720)/(40) = 18`

The measure of angles are:

`4x = 4 * 18 = 72^(\circ)\\5x = 5 * 18 = 90^(\circ)\\5x = 5 * 18 = 90^(\circ)\\8x = 8 * 18 = 144^(\circ)\\9x = 9 * 18 = 162^(\circ)\\9x = 9 * 18 = 162^(\circ)`

Therefore; the measure of the smallest angle in the hexagon is,
`72^(\circ)`