Answer:
[tex]72^{\circ}[/tex] is the measure of the smallest angle in the hexagon.
Step-by-step 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
⇒[tex]4x+5x+5x+8x+9x+9x = 720^{\circ}[/tex]
Combine like terms;
[tex]40x = 720^{\circ}[/tex]
Divide both sides by 40 we get;
[tex]x = \frac{720}{40} = 18[/tex]
The measure of angles are:
[tex]4x = 4 \times 18 = 72^{\circ}\\5x = 5 \times 18 = 90^{\circ}\\5x = 5 \times 18 = 90^{\circ}\\8x = 8 \times 18 = 144^{\circ}\\9x = 9 \times 18 = 162^{\circ}\\9x = 9 \times 18 = 162^{\circ}[/tex]
Therefore; the measure of the smallest angle in the hexagon is, [tex]72^{\circ}[/tex]
