Liam is correct, as the sum of the exterior angles for both polygons (heptagon and decagon) is the same that is 360°.
"An exterior angle is the angle between a side of a polygon and an extended adjacent side."
"A decagon is a polygon having ten sides, ten interior angles and ten vertices."
"A heptagon can be defined as a polygon having seven sides, seven interior angles and seven vertices."
First consider a decagon,
The interior angle of decagon is 144° , so the corresponding exterior angle is 36°.
In decagon there are ten interior angles. So, there are 10 exterior angles.
So, sum of the exterior angles of a decagon is, 10 × 36 = 360°
Now, consider a heptagon.
The interior angle of heptagon is 5π/7 radians which is approximately 128.57°.
The corresponding exterior angle of heptagon is 2π/7 radians ≈ 51.43°
In heptagon, there are seven interior angles. So, there must be corresponding 7 exterior angles.
So, sum of the exterior angles of a heptagon is, 2π/7 × 7 = 2π
that is, 360°.
Hence, the sum of the exterior angles for both polygons is the same.
This means, Liam is correct.
Learn more about exterior angles here:
https://brainly.com/question/11379452
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