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Directions: Study the following questions and choose the right answer:
1
Measure of each interior angle of a regular polygon can never be :
» Explain it
B
Check through the options, each interior angle

= {180º – (360º / n)}

If measure of each angle = 105°, then

180º – (360º / n) = 105º

180° × n – 360° = 105° × n

75° × n = 360°

n = (24 / 5)

which is impossible

Hence, option B is correct.

2
The sum of all interior angles of a regular polygon is twice the sum of all its exterior angles. The number of sides of the polygon is
» Explain it
D
Let the number of sides of a polygon be n. Then,

Sum of interior angles = (2n – 4) × 90°

Sum of exterior angles = 360°

∴  (2n – 4) × 90° = 2 × 360°

2n – 4 = 8

2n = 12

n = 6

Hence, option D is correct.

3
The ratio between the number of sides of two regular polygons is 1 : 2 and the ratio between their interior angles is 2 : 3. The number of sides of these polygons is respectively
» Explain it
C
Let the number of sides of two regular polygons be x and 2x respectively. Then,

{180º – (360º / x)} : { 180º – (360º / 2x) = 2:3

{180º (x – 2) / x} × {x / 180º (x – 1)} = 2 / 3

3x – 6 = 2x – 2

x = 4

∴  Number of sides = x = 4 and 2x = 2 × 4 = 8

Hence, option C is correct.

4
There are two regular polygons with number of sides equal to (n – 1) and (n + 2). Their exterior angles differ by 6°. The value of n is 
» Explain it
C
{360º / (n – 1)} – {360º (n + 2)} = 6º

360º [( n + 2 – n + 1 ) / {(n – 1) (n + 2)}] = 6º

(n – 1) (n + 2) = 180

n2 + n – 2 = 180

n2 + n – 182 = 0

n2 + 14n – 13n – 182 = 0

n(n + 14) – 13(n + 14) = 0

(n – 13) (n + 14) = 0

n = 13, – 14      [∵  n ≠ – 14 ]

Hence, optino C is correct.

5
If each interior angle of a regular polygon is 150°, the number of sides of the polygon is
» Explain it
D
Let the number of sides of a regular polygon be n. Then,

180º – (360º / n) = 150º

180° × n – 360° = 150° × n

30° × n = 360°

n = 12

Hence, option D is correct.