Answer:
Part I : 2160°
Part II : 165°
Part III : 36 sides.
Part IV : 10 sides.
Step-by-step explanation:
Part I : If the polygon has 14 sides, then the sum of all the interior angles of a polygon will be = (14 - 2) × 180° = 2160°. (Answer)
Part II : If the polygon has 24 sides, then the sum of all the interior angles of a polygon will be = (24 - 2) × 180° = 3960°.
Therefore, the measurement of each interior angles will be = [tex]\frac{3960}{24} = 165^{\circ}[/tex]. (Answer)
Part III : Given that 10° is each exterior angle of a polygon. So, each interior angle is (180 - 10) = 170°.
If the number of sides is n, then,
[tex]\frac{(n - 2) \times 180}{n} = 170[/tex]
⇒ 10n = 360
⇒ n = 36 sides. (Answer)
Part IV : Sum of the all interior angles is 1440°.
If it has n sides, then (n - 2) \times 180 = 1440
⇒ n - 2 = 8
⇒ n = 10 (Answer)
