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SAT II Math II : 2-Dimensional Geometry

Study concepts, example questions & explanations for SAT II Math II

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2 Diagnostic Tests 130 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #2 : Finding Angles

What angle do the minute and hour hands of a clock form at 4:15?

Possible Answers:

$27\frac{1}{2} ^{\circ }$

$32\frac{1}{2} ^{\circ }$

$40 ^{\circ }$

$37\frac{1}{2} ^{\circ }$

$30 ^{\circ }$

Correct answer:

$37\frac{1}{2} ^{\circ }$

Explanation:

There are twelve numbers on a clock; from one to the next, a hand rotates $\left (\frac{360}{12} \right )^{\circ } = 30^{\circ }$ . At 4:15, the minute hand is exactly on the "3" - that is, on the $\left (30 \times 3 \right )^{\circ }= 90^{\circ }$ position. The hour hand is one-fourth of the way from the "4" to the "5" - that is, on the $\left (4 \frac{1}{4} \times 30 \right )^{\circ } = 127 \frac{1}{2} ^{\circ }$ position. Therefore, the difference is the angle they make:

$127 \frac{1}{2} ^{\circ } - 90^{\circ } = 37 \frac{1}{2}^{\circ }$ .

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Example Question #1 : Finding Angles

If the vertical angles of intersecting lines are: 2x-9 and 3x+6 , what must be the value of ?

Possible Answers:

$\frac{93}{5}$

$\frac{183}{5}$

Correct answer:

Explanation:

Vertical angles of intersecting lines are always equal.

Set the two expressions equal to each other and solve for .

2x-9 = 3x+6

Subtract from both sides.

2x-9 -2x= 3x+6-2x

-9 = x+6

Subtract 6 from both sides.

-9 -6= x+6-6

The answer is:

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Example Question #3 : Finding Angles

If the angles in degrees are x+3 and x+7 which are complementary to each other, what is three times the value of the smallest angle?

Possible Answers:

129

255

120

264

141

Correct answer:

129

Explanation:

Complementary angles add up to 90 degrees.

Set up an equation such that the sum of both angles equal to 90.

x+3+x+7 = 90

2x+10 = 90

Subtract 10 from both sides.

2x+10 -10= 90-10

2x=80

Divide by 2 on both sides.

$\frac{2x}{2}=\frac{80}{2}$

x=40

The angles are:

x+3 = 40+3 = 43

x+7 = 40+7 = 47

Three times the value of the smallest angle is:

$43\times 3 = 129$

The answer is: 129

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Example Question #1 : Finding Angles

If the angles -10x-5 and are supplementary, what must be the value of ?

Possible Answers:

$\frac{37}{3}$

$-\frac{37}{3}$

Correct answer:

Explanation:

Supplementary angles sum up to 180 degrees.

-10x-5+5x = 180

-5x-5 = 180

Add five on both sides.

-5x-5 +5= 180+5

-5x = 185

Divide by negative five on both sides to determine .

$\frac{-5x}{-5} = \frac{185}{-5}$

x=-37

The answer is:

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Example Question #11 : Finding Angles

Suppose a set of intersecting lines. If an angle is 120 degrees, what must be the sum of the adjacent angle and the vertical angle to the given angle?

Possible Answers:

$240^\circ$

$200^\circ$

$220^\circ$

$180^\circ$

$360^\circ$

Correct answer:

$180^\circ$

Explanation:

In an intersecting pair of lines, recall that vertical angles will always equal.

$\textup{Vertical angle } = 120$

The adjacent angle with the given angle will form a straight line, and both of the angles must sum to 180 degrees.

Subtract 120 from 180 to get the adjacent angle.

180-120 = 60

Sum the two angles.

120+60 = 180

The answer is: 180

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Example Question #61 : 2 Dimensional Geometry

If a set of angles are supplementary, what must be the other angle if a given angle is ?

Possible Answers:

$55^\circ$

$215^\circ$

$145^\circ$

$155^\circ$

$135^\circ$

Correct answer:

$145^\circ$

Explanation:

Supplementary angles must add up to 180 degrees.

To find the missing angle, subtract the known angle from 180 degrees.

180-35 = 145

The answer is: $145^\circ$

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Example Question #13 : Finding Angles

If two angles of a triangle are $\frac{2}{3}\pi, \frac{1}{4}\pi$ radians, what must be the other angle in degrees?

Possible Answers:

Correct answer:

Explanation:

Every pi radians equal 180 degrees.

We can choose to convert the radians to degrees first.

$\frac{2}{3}\pi = \frac{2}{3}(180) = 120$

$\frac{1}{4}\pi = \frac{1}{4}(180) = 45$

The sum of these two angles are:

120+45 = 165

Subtract this value from 180 to determine the third angle.

180-165 = 15

The answer is:

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Example Question #1 : Analyzing Figures

Thingy_5

Refer to the above diagram. Which of the following is not a valid name for $\angle DBF$ ?

Possible Answers:

$\angle B$

All of the other choices give valid names for the angle.

$\angle FBE$

$\angle FBD$

$\angle CBF$

Correct answer:

$\angle B$

Explanation:

$\angle B$ is the correct choice. A single letter - the vertex - can be used for an angle if and only if that angle is the only one with that vertex. This is not the case here. The three-letter names in the other choices all follow the convention of the middle letter being vertex and each of the other two letters being points on a different side of the angle.

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Example Question #62 : 2 Dimensional Geometry

Triangle

Use the rules of triangles to solve for x and y.

Possible Answers:

x=30, y=60

x=30, y=30

x=60, y=30

x=45, y=45

Correct answer:

x=60, y=30

Explanation:

Using the rules of triangles and lines we know that the degree of a straight line is 180. Knowing this we can find x by creating and solving the following equation:

x=180-120

x=60

Now using the fact that the interior angles of a triangle add to 180 we can create the following equation and solve for y:

y=180-(90+60)

y=180-150

y=30

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Example Question #63 : 2 Dimensional Geometry

Circle

Use the facts of circles to solve for x and y.

Possible Answers:

x=13, y=10

x=39.5, y=11

x=10, y=30

x=11, y= 39.5

Correct answer:

x=11, y= 39.5

Explanation:

In this question we use the rule that oppisite angles are congruent and a line is 180 degrees. Knowing these two facts we can first solve for x then solve for y.

2x=22

x=11

Then:

4y+2x=180

4y+2(11)=180

4y+22=180

4y=158

y=39.5

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SAT II Math II : 2-Dimensional Geometry

Study concepts, example questions & explanations for SAT II Math II

All SAT II Math II Resources

Example Questions

Example Question #2 : Finding Angles

Example Question #1 : Finding Angles

Example Question #3 : Finding Angles

Example Question #1 : Finding Angles

Example Question #11 : Finding Angles

Example Question #61 : 2 Dimensional Geometry

Example Question #13 : Finding Angles

Example Question #1 : Analyzing Figures

Example Question #62 : 2 Dimensional Geometry

Example Question #63 : 2 Dimensional Geometry

All SAT II Math II Resources

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