The sides of a regular polygon are congruent.
The size of STR is 15 degrees
The polygon is 12-sided.
This means that:
[tex]\mathbf{n =12}[/tex]
The sum of angles in a regular hexagon is 360.
So, the angle at vertex S is:
[tex]\mathbf{\theta = \frac{360}{n}}[/tex]
This gives
[tex]\mathbf{\theta = \frac{360}{12}}[/tex]
[tex]\mathbf{\theta = 30^o}[/tex]
The external angle of a triangle equals the sum of the opposite internal angles.
This means that:
[tex]\mathbf{\theta = \angle STR + \angle SRT}[/tex]
Where:
[tex]\mathbf{ \angle STR = \angle SRT}[/tex]
So, we have:
[tex]\mathbf{\theta = \angle STR + \angle STR}[/tex]
[tex]\mathbf{\theta = 2\angle STR}[/tex]
Substitute [tex]\mathbf{\theta = 30^o}[/tex]
[tex]\mathbf{30^o = 2\angle STR}[/tex]
Divide both sides by 2
[tex]\mathbf{15^o = \angle STR}[/tex]
Rewrite as:
[tex]\mathbf{\angle STR = 15^o }[/tex]
Hence, the size of STR is 15 degrees
Read more about angles in a polygon at:
https://brainly.com/question/19023938
