ISEE Upper Level Math : Other Quadrilaterals

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

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Example Questions

Example Question #1 : Other Quadrilaterals

Three of the interior angles of a quadrilateral measure , and . What is the measure of the fourth interior angle?

Possible Answers:

This quadrilateral cannot exist.

Correct answer:

Explanation:

The measures of the angles of a quadrilateral have sum . If  is the measure of the unknown angle, then:

The angle measures .

Example Question #2 : Other Quadrilaterals

The angles of a quadrilateral measure . Evaluate .

Possible Answers:

Correct answer:

Explanation:

The sum of the degree measures of the angles of a quadrilateral is 360, so we can set up and solve for  in the equation:

Example Question #3 : Other Quadrilaterals

The four angles of a quadrilateral have the following value: 79 degrees, 100 degrees, 50 degrees, and  degrees. What is the value of ?

Possible Answers:

Correct answer:

Explanation:

Given that there are 360 degrees when all the angles of a quadrilateral are added toghether, this problem can be solved with the following equation:

Example Question #4 : Other Quadrilaterals

In a quadrilateral, the angles have the following values:

What is the value of ?

Possible Answers:

Correct answer:

Explanation:

Given that there are 360 degrees when the angles of a quadrilateral are added together, it follows that:

Example Question #231 : Plane Geometry

The perimeter of a quadrilateral is 86. The four sides measure

.

What is the value of ?

Possible Answers:

Correct answer:

Explanation:

Given that the perimeter is 86, the sides of the quadrilateral will all add up to this amount. 

The first step is the add together all the integers. 

Next, we subtract 70 from each side. 

We reduce the left side of the equation:

Now, we divide each side by 4. This leaves:

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