ISEE Upper Level Quantitative : Geometry
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Example Questions
Example Question #1 : How To Find Area
The above rectangle, which has perimeter 360, is divided into squares of equal size. Give the area of the shaded portion.
The sides of the rectangle, in total, are divided into 18 segments of equal measure, as indicated below:
The rectangle has a total perimeter of 360, so each segment - one side of a square - measures 
Example Question #111 : Isee Upper Level (Grades 9 12) Quantitative Reasoning
Seven angles of a convex octagon are congruent; the measure of the eighth is twice that of any one of the other seven. What is the measure of that eighth angle?
This octagon cannot exist.
This octagon cannot exist.
Let 
The angle measures of any convex octagon must add up to 
Therefore, the largest angle must measure 
Example Question #11 : Other Polygons
Which is the greater quantity?
(a) The sum of the measures of the exterior angles of a thirty-sided polygon, one per vertex
(b) The sum of the measures of the exterior angles of a forty-sided polygon, one per vertex
(a) and (b) are equal
(b) is greater
(a) is greater
It is impossible to tell from the information given
(a) and (b) are equal
The Polygon Exterior-Angle Theorem states that the sum of the measures of the exterior angles of any polygon, one per vertex, is 
Example Question #111 : Geometry
Which is the greater quantity?
(a) The measure of an interior angle of an equilateral triangle
(b) The measure of an exterior angle of a regular octagon
(a) and (b) are equal.
(a) is greater.
It is impossible to tell from the information given.
(b) is greater.
(a) is greater.
Each angle of an equilateral triangle measures 
The sum of the exterior angles of any polygon, one per vertex, is 
This makes (a) greater.
Example Question #13 : Other Polygons
A regular polygon has exterior angles that measure 
(a) The number of sides of this polygon
(b) 16
(a) and (b) are equal
It is impossible to tell from the information given
(b) is greater
(a) is greater
(a) is greater
A regular polygon with 16 sides has exterior angles measuring
The polygon in (a) has exterior angles that are narrower, so it must have more than 16 sides. (a) is greater.
Example Question #14 : Other Polygons
A regular polygon has interior angles that are obtuse. Which is the greater quantity?
(a) The number of sides of the polygon
(b) 4
(a) and (b) are equal
(a) is greater
It is impossible to tell from the information given
(b) is greater
(a) is greater
A regular four-sided polygon - a square - has four right angles; a regular triangle is equiangular and has three acute ( 
Any regular polygon with five sides or more has congruent angles that measure at least 
Example Question #15 : Other Polygons
A regular polygon has interior angles that measure 
(a) The number of sides of the polygon
(b) 24
(a) is greater
It is impossible to tell from the information given
(a) and (b) are equal
(b) is greater
(a) and (b) are equal
A regular polygon with 24 sides has interior angles measuring
Therefore, the polygon in (a) has 24 sides, and the quantities are equal.
Example Question #16 : Other Polygons
Polygon C is regular. If one exterior angle is taken at each vertex, and the degree measures are added, the sum is 360. Which of the following is the greater quantity?
(a) 12
(b) The number of sides of Polygon C
(b) is the greater quantity
(a) is the greater quantity
It cannot be determined which of (a) and (b) is greater
(a) and (b) are equal
It cannot be determined which of (a) and (b) is greater
In any regular (or other convex) polygon, regardless of the number of sides in the polygon, the sum of the measures of the exterior angles, one per vertex, is 
Example Question #112 : Geometry
Polygon B is regular. The measure of each exterior angle of Polygon B is 
(a) The number of sides of Polygon B
(b) 12
(a) is the greater quantity
It cannot be determined which of (a) and (b) is greater
(b) is the greater quantity
(a) and (b) are equal
(a) and (b) are equal
In any polygon, the sum of the measures of the exterior angles, one per vertex, is 
and
This means the polygon has 12 sides, making the quantities equal.
Example Question #118 : Geometry
Polygon A is a regular polygon with interior angles of measure 
Which is the greater quantity?
(a) The number of sides of Polygon A
(b) 10
It cannot be determined which of (a) and (b) is greater
(a) and (b) are equal
(a) is the greater quantity
(b) is the greater quantity
(b) is the greater quantity
If a regular polygon - one with congruent sides and congruent angles - has interior angles of measure 
and
This means the polygon has 9 sides, making (b) the greater quantity.
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