ISEE Upper Level Quantitative : Other Quadrilaterals

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

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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 measure of the fourth angle is .

Example Question #2 : Quadrilaterals

In a certain quadrilateral, three of the angles are , , and . What is the measure of the fourth angle?

Possible Answers:

Correct answer:

Explanation:

A quadrilateral has four angles totalling . So, first add up the three angles given. The sum is . Then, subtract that from 360. This gives you the missing angle, which is .

Example Question #2 : Other Quadrilaterals

The angles of Quadrilateral A measure 

The angles of Pentagon B measure 

Which is the greater quantity?

(A) 

(B) 

Possible Answers:

(A) and (B) are equal

(B) is greater

(A) is greater

It is impossible to determine which is greater from the information given

Correct answer:

(B) is greater

Explanation:

The sum of the measures of the angles of a quadrilateral is ; the sum of the measures if a pentagon is . Therefore, 

and 

, so (B) is greater.

Example Question #3 : 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 measure of the fourth angle is .

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