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ISEE Upper Level Quantitative : Other Quadrilaterals

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Example Questions

Example Question #1 : Other Quadrilaterals

Three of the interior angles of a quadrilateral measure $100 ^{\circ }$ , $105^{\circ }$ , and $110 ^{\circ }$ . What is the measure of the fourth interior angle?

Possible Answers:

$15 ^{\circ }$

$35^{\circ }$

$25^{\circ }$

$45^{\circ }$

This quadrilateral cannot exist.

Correct answer:

$45^{\circ }$

Explanation:

The measures of the angles of a quadrilateral have sum $360^{\circ }$ . If is the measure of the unknown angle, then:

x + 100 + 105 + 110 = 360

x + 315= 360

x + 315-315= 360-315

x = 45

The measure of the fourth angle is $45^{\circ }$ .

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Example Question #2 : Quadrilaterals

In a certain quadrilateral, three of the angles are $65^{\circ}$ , $120^{\circ}$ , and $34^{\circ}$ . What is the measure of the fourth angle?

Possible Answers:

$29^{\circ}$

$219^{\circ}$

$141^{\circ}$

$139^{\circ}$

$41^{\circ}$

Correct answer:

$141^{\circ}$

Explanation:

A quadrilateral has four angles totalling $360^{\circ}$ . So, first add up the three angles given. The sum is $219^{\circ}$ . Then, subtract that from 360. This gives you the missing angle, which is $141^{\circ}$ .

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Example Question #2 : Quadrilaterals

The angles of Quadrilateral A measure $80^{\circ }, 80^{\circ }, 80^{\circ }, x^{\circ }$

The angles of Pentagon B measure $100^{\circ }, 100^{\circ }, 100^{\circ }, 100^{\circ }, y^{\circ }$

Which is the greater quantity?

(A)

(B)

Possible Answers:

(A) is greater

(B) is greater

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

(A) and (B) are equal

Correct answer:

(B) is greater

Explanation:

The sum of the measures of the angles of a quadrilateral is $360^{\circ }$ ; the sum of the measures if a pentagon is $540^{\circ }$ . Therefore,

x + 80 + 80 + 80 = 360

x + 240 = 360

x = 120

and

y + 100+ 100+ 100+ 100 = 540

y + 4 00 = 540

y = 140

y > x , so (B) is greater.

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Example Question #3 : Quadrilaterals

Three of the interior angles of a quadrilateral measure $100 ^{\circ }$ , $105^{\circ }$ , and $110 ^{\circ }$ . What is the measure of the fourth interior angle?

Possible Answers:

$45^{\circ }$

This quadrilateral cannot exist.

$25^{\circ }$

$15 ^{\circ }$

$35^{\circ }$

Correct answer:

$45^{\circ }$

Explanation:

The measures of the angles of a quadrilateral have sum $360^{\circ }$ . If is the measure of the unknown angle, then:

x + 100 + 105 + 110 = 360

x + 315= 360

x + 315-315= 360-315

x = 45

The measure of the fourth angle is $45^{\circ }$ .

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All ISEE Upper Level Quantitative Resources

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ISEE Upper Level Quantitative : Other Quadrilaterals

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

All ISEE Upper Level Quantitative Resources

Example Questions

Example Question #1 : Other Quadrilaterals

Example Question #2 : Quadrilaterals

Example Question #2 : Quadrilaterals

Example Question #3 : Quadrilaterals

All ISEE Upper Level Quantitative Resources

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