GMAT Math : DSQ: Calculating an angle in a polygon

Study concepts, example questions & explanations for GMAT Math

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Example Questions

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Example Question #11 : Dsq: Calculating An Angle In A Polygon

A nonagon is a nine-sided polygon.

Is Nonagon  regular?

Statement 1: 

Statement 2: 

Possible Answers:

EITHER statement ALONE is sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

Correct answer:

EITHER statement ALONE is sufficient to answer the question.

Explanation:

Each angle of a regular nonagon measures 

Therefore, each of the two statements proves that the nonagon is not regular.

Example Question #12 : Dsq: Calculating An Angle In A Polygon

What is the measure of   ? 

Statement 1:  is an exterior angle of an equilateral triangle.

Statement 2:  is an interior angle of a regular hexagon.

Possible Answers:

EITHER statement ALONE is sufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

Correct answer:

EITHER statement ALONE is sufficient to answer the question.

Explanation:

An exterior angle of an equilateral triangle measures . An interior angle of a regular hexagon measures . Either statement is sufficient.

Example Question #21 : Polygons

Pentagon

Note: Figure NOT drawn to scale.

Refer to the above figure. Is Pentagon  regular?

Statement 1: 

Statement 2: 

Possible Answers:

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

Correct answer:

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

Explanation:

If a shape is regular, that means that all of its sides are equal. It also means that all of its interior angles are equal. Finally, if all of the interior angles are equal, then the exterior angles will all be equal to each other as well.

In a regular polygon, we can find the measure of ANY exterior angle by using the formula

where is equal to the number of sides.

Each exterior angle of a regular (five-sided) pentagon measures

  

Statement 1 alone neither proves nor disproves that the pentagon is regular. We now know that one exterior angle is , but we do not know if any of the other exterior angles are also .

Statement 2, however, proves that the pentagon is not regular, as it has at least one exterior angle that does not have measure .

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