ISEE Upper Level Math : How to find an angle in a pentagon

Study concepts, example questions & explanations for ISEE Upper Level Math

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Example Questions

Example Question #1 : How To Find An Angle In A Pentagon

A convex pentagon has four angles that measure  each. What is the measure of the fifth angle?

Possible Answers:

This pentagon cannot exist.

Correct answer:

This pentagon cannot exist.

Explanation:

The angles of a pentagon measure a total of . If we let the unknown angle measure be , then from this information:

Since an angle measure cannot be negative, this pentagon cannot exist.

Example Question #2 : How To Find An Angle In A Pentagon

The measures of the angles of a pentagon are . If , what is ?

Possible Answers:

This pentagon cannot exist.

Correct answer:

Explanation:

The angles of a pentagon measure a total of . From the information, we know that:

If , then 

Example Question #3 : How To Find An Angle In A Pentagon

The measures of the angles of a pentagon are . If , what is ?

Possible Answers:

This pentagon cannot exist.

Correct answer:

Explanation:

The angles of a pentagon measure a total of . From the information, we know:

If , then the above becomes:

Example Question #4 : How To Find An Angle In A Pentagon

Solve for :

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Possible Answers:

Correct answer:

Explanation:

The sum of the interior angles of a pentagon can be determined by the following equation, where  is the number of sides:

Therefore:

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