DSQ: Calculating an angle in a polygon - GMAT Quantitative

The sum of the measures of the six interior angles of any hexagon is , so if Statement 1 is true, then the sum of the six numbers is 720, regardless of the individual values.

Statement 2 is not enough, however, for us to deduce this sum; this only tells us the mean of the third- and fourth-highest values.

The sum of the measures of the six interior angles of any hexagon is , so if Statement 1 is true, then the sum of the six numbers is 720, regardless of the individual values.

Statement 2 is not enough, however, for us to deduce this sum; this only tells us the mean of the third- and fourth-highest values.

The sum of the measures of the five interior angles of any pentagon is , so if Statement 1 is true, then the sum of the five numbers is 540, regardless of the individual values.

The mean of five data values multiplied by 5 is the sum of the values, so if Statement 2 is true, then their sum is .

The sum of the measures of the six interior angles of any hexagon is , so if Statement 1 is true, then the sum of the six numbers is 720, regardless of the individual values.

Statement 2 is not enough, however, for us to deduce this sum; this only tells us the mean of the third- and fourth-highest values.

The sum of the measures of the five interior angles of any pentagon is , so if Statement 1 is true, then the sum of the five numbers is 540, regardless of the individual values.

The mean of five data values multiplied by 5 is the sum of the values, so if Statement 2 is true, then their sum is .

The sum of the measures of the six interior angles of any hexagon is , so if Statement 1 is true, then the sum of the six numbers is 720, regardless of the individual values.

Statement 2 is not enough, however, for us to deduce this sum; this only tells us the mean of the third- and fourth-highest values.

The sum of the measures of the five interior angles of any pentagon is , so if Statement 1 is true, then the sum of the five numbers is 540, regardless of the individual values.

The mean of five data values multiplied by 5 is the sum of the values, so if Statement 2 is true, then their sum is .

The sum of the measures of the six interior angles of any hexagon is , so if Statement 1 is true, then the sum of the six numbers is 720, regardless of the individual values.

Statement 2 is not enough, however, for us to deduce this sum; this only tells us the mean of the third- and fourth-highest values.

The sum of the measures of the five interior angles of any pentagon is , so if Statement 1 is true, then the sum of the five numbers is 540, regardless of the individual values.

The mean of five data values multiplied by 5 is the sum of the values, so if Statement 2 is true, then their sum is .

The sum of the measures of the six interior angles of any hexagon is , so if Statement 1 is true, then the sum of the six numbers is 720, regardless of the individual values.

Statement 2 is not enough, however, for us to deduce this sum; this only tells us the mean of the third- and fourth-highest values.

The sum of the measures of the five interior angles of any pentagon is , so if Statement 1 is true, then the sum of the five numbers is 540, regardless of the individual values.

The mean of five data values multiplied by 5 is the sum of the values, so if Statement 2 is true, then their sum is .

The sum of the measures of the six interior angles of any hexagon is , so if Statement 1 is true, then the sum of the six numbers is 720, regardless of the individual values.

Statement 2 is not enough, however, for us to deduce this sum; this only tells us the mean of the third- and fourth-highest values.

The sum of the measures of the five interior angles of any pentagon is , so if Statement 1 is true, then the sum of the five numbers is 540, regardless of the individual values.

The mean of five data values multiplied by 5 is the sum of the values, so if Statement 2 is true, then their sum is .

The sum of the measures of the six interior angles of any hexagon is , so if Statement 1 is true, then the sum of the six numbers is 720, regardless of the individual values.

Statement 2 is not enough, however, for us to deduce this sum; this only tells us the mean of the third- and fourth-highest values.

The sum of the measures of the five interior angles of any pentagon is , so if Statement 1 is true, then the sum of the five numbers is 540, regardless of the individual values.

The mean of five data values multiplied by 5 is the sum of the values, so if Statement 2 is true, then their sum is .

The sum of the measures of the angles of a hexagon is

Therefore,

Suppose we only know that , , and are the first three terms of an arithmetic sequence, in order. Then for some common difference ,

Suppose we only know that . Then

With no further information, we cannot determine .

The relationship between the number of sides of a regular polygon and the measure of a single angle is

If we are given that , then we can substitute and solve for :

making the figure a nine-sided polygon.

Knowing only the measure of each side is neither necessary nor helpful; for example, it is possible to construct an equilateral triangle with sidelength 8 or a square with sidelength 8.

The correct answer is that Statement 1 alone is sufficient to answer the question, but not Statement 2 alone.

Information about the hexagon is irrelevant, so Statement 2 has no bearing on the answer to the question.

The measures of the exterior angles of any pentagon, one per vertex, total , and they are congruent if the pentagon is regular, so if this is the case, each would measure . But if Statement 1 is true, then an exterior angle of the pentagon measures . Therefore, Statement 1 is enough to answer the question in the negative.

To show that the rhombus is a square, you need to demonstrate that one of its angles is a right angle - that is, . Both statements together are insufficent - if , you would need to demonstrate that is true or false, and the fact that the triangle is not equilateral is not enough to prove or to disprove this.