Question

Q 28. The question given below is followed by two statements numbered I and II. Determine if the statements are, individually or
together, sufficient to answer the question.
Question: What is the number of sides of a regular polygon?
Statements:
I. The sum of all its internal angles is 540°.
II. The angle subtended by all the sides at the centre is equal to 72º.
Ops: A. O Both statements I and II together are sufficient to answer the question asked but neither statement alone is sufficient.
B. O Statements I and II together are not sufficient to answer the question asked and additional data to the problem is neede
C. Each statement alone is sufficient to answer the question.
D. OOnly one of the statements, alone, is sufficient to answer the question but the other statement is not.​

Answer 1

Step-by-step explanation:

O Both statements I and II together are sufficient to answer the question asked but neither statement alone is sufficient.

B. O Statements I and II together are not sufficient to answer the question asked and additional data to the problem is neede

C. Each statement alone is sufficient to answer the question.

D. OOnly one of the statements, alone, is sufficient to answer the question but the other statement is not.

Answer 2

Option (d) is the correct answer.
Only one of the statements, alone, is sufficient to answer the question but the other statement is not.

Statement 1 is the only statement that is sufficient to answer the question.

We know that,
The sum of all the interior angles of a regular polygon = (n - 2) * 180

If we know the sum of all the interior angles of a polygon, then we can easily find the number of sides of that polygon.
Given, the sum of all the interior angles = 540°
⇒ 540° = (n - 2)
    180°
⇒ 3 = n - 2
⇒ n = 3 + 2
⇒ n = 5

∴ The number of sides of the polygon whose sum of all the interior angles is given = 5.
⇒ It is a pentagon.

→ We can say that only statement 1 is sufficient to answer the question.

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