GMAT Math : Calculating an angle in a polygon

Study concepts, example questions & explanations for GMAT Math

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Example Questions

Example Question #701 : Gmat Quantitative Reasoning

Pentagon

Note: Figure NOT drawn to scale.

Given Regular Pentagon . What is  ?

Possible Answers:

Correct answer:

Explanation:

Quadrilateral  is a trapezoid, so  .

, so

Example Question #11 : Calculating An Angle In A Polygon

The angles of a pentagon measure .

Evaluate .

Possible Answers:

This pentagon cannot exist

Correct answer:

Explanation:

The sum of the degree measures of the angles of a (five-sided) pentagon is , so we can set up and solve the equation:

Example Question #702 : Gmat Quantitative Reasoning

The measures of the angles of a pentagon are: 

What is  equal to?

Possible Answers:

Correct answer:

Explanation:

The degree measures of the interior angles of a pentagon total , so

Example Question #12 : Calculating An Angle In A Polygon

What is the measure of an angle in a regular octagon?

Possible Answers:

Correct answer:

Explanation:

On octagon has  sides. The word regular means that all of the angles are equal. Therefore, we can use the general equation for finding the angle measurement of a regular polygon:

, where  is the number of sides of the polygon.

.

Example Question #11 : Calculating An Angle In A Polygon

What is the measure of one exterior angle of a regular twenty-four sided polygon?

Possible Answers:

Correct answer:

Explanation:

The sum of the measures of the exterior angles of any polygon, one at each vertex, is . Since a regular polygon with twenty-four sides has twenty-four congruent angles, and therefore, congruent exterior angles, just divide:

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