Question

Which of the following statements is not correct?<br />(a) If the sum of angles of a n sided polygon is n right angles, then n = 4.<br />(b) No regular polygon can have an integer angle equal to 110°<br />(c) A regular polygon with q80 sides have each interior angle equal to 178°.<br />(d) No regular polygon can have interior angle equal to 140°.​
Explain also​

Answer 1

Answer:

(a) Sum of angles of an n sided polygon = (n – 2) × 180°

Given, (n – 2) × 180° = n × 90°

=> 2(n – 2) = n

=> 2n – 4 = n

=> n = 4

(b) Each interior angle of a regular polygon of n sides

(n – 2)/n × 180°

=> (n – 2)n × 180° = 110°

=> 180°n – 360° = 110°n

=> 70°n = 360°

=> n = 360°/70°

$= 5 \times \frac{1}{7}$

It is not a whole number. Hence the given angle cannot be the interior angle of a regular polygon.

(c) Interior angle of a regular polygon with 180 sides

(180 – 2)/180 × 180°

= 178 × 1°

= 178°.

(d) Check as in option (b)

Hence option (b) is not correct.