GMAT Math : Geometry

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Example Questions

Example Question #9 : Understanding Rays

Thingy

Name a pair of opposite rays in the above figure.

Possible Answers:

$\overrightarrow{ON}$ and $\overrightarrow{OX}$

$\overrightarrow{EO}$ and $\overrightarrow{GO}$

$\overrightarrow{OA}$ and $\overrightarrow{OG}$

$\overrightarrow{HE}$ and $\overrightarrow{ON}$

$\overrightarrow{HO}$ and $\overrightarrow{HA}$

Correct answer:

$\overrightarrow{ON}$ and $\overrightarrow{OX}$

Explanation:

Opposite rays are rays that have the same endpoint are on the same line, but share only the endpoint.

Two names of opposite rays must begin with the same letter, since the first letter in the name of a ray is the endpoint. Also, the second letters must represent points collinear with each other and the endpoint, and on opposite sides of the shared endpoint. Of the five choices, only $\overrightarrow{ON}$ and $\overrightarrow{OX}$ together meet this criteria.

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Example Question #10 : Understanding Rays

Thingy

In the above figure, which of the following gives a correct name for the union of $\overrightarrow{OX}$ and $\overrightarrow{OG}$ ?

Possible Answers:

$\angle GXO$

$\angle XOG$

$\angle XGO$

$\overline{XG}$

$\overleftrightarrow{XG}$

Correct answer:

$\angle XOG$

Explanation:

$\overrightarrow{OX}$ and $\overrightarrow{OG}$ are noncollinear rays with the same endpoint, so their union is an angle. The shared endpoint of the rays, which here is , is the vertex of the formed angle, and is therefore the middle letter of the name of the angle; this letter is flanked by two letters representing one point on each ray, which are and . The correct choice among those given is $\angle XOG$ .

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Example Question #21 : Lines

Thingy

In the above figure, give the union of $\overrightarrow{GE}$ and $\overrightarrow{OE}$ .

Possible Answers:

$\overrightarrow{OE}$

$\overrightarrow{GE}$

$\overline{OE}$

$\overline{GO}$

$\overleftrightarrow{GE}$

Correct answer:

$\overrightarrow{GE}$

Explanation:

$\overrightarrow{OE}$ can be seen to be completely contained in $\overrightarrow{GE}$ - that is, $\overrightarrow{OE}\subseteq \overrightarrow{GE}$ . The union of a set and its subset is the containing set, so the correct response is $\overrightarrow{GE}$ .

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Example Question #22 : Lines

Thingy

Give the union of $\overrightarrow{NO}$ and $\overrightarrow{XO}$ in the above figure.

Possible Answers:

$\overrightarrow{NO}$

$\overline{NX}$

$\overleftrightarrow{NX}$

$\overline{XO}$

$\overrightarrow{XO}$

Correct answer:

$\overleftrightarrow{NX}$

Explanation:

The diagram below shows $\overrightarrow{NO}$ and $\overrightarrow{XO}$ in red and green, respectively:

Thingy_x

The union of the two sets is the set of points in one or the other; this set is the entire line containing the two rays, which is $\overleftrightarrow{NX}$ .

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Example Question #653 : Problem Solving Questions

Thingy

In the above figure, let be the midpoint of $\overline{EO}$ . Which of the following would give another name for $\overrightarrow{GM}$ ?

Possible Answers:

$\overrightarrow{OE}$

$\overrightarrow{ME}$

$\overrightarrow{EM}$

$\overrightarrow{GE}$

$\overrightarrow{MG}$

Correct answer:

$\overrightarrow{GE}$

Explanation:

Below is the diagram with midpoint of $\overline{EO}$ added; also, $\overrightarrow{GM}$ , the ray starting at and passing through , is in green.

Thingy x

A ray is named after, in order, its endpoint and any other point on the ray. $\overrightarrow{GM}$ has as an endpoint, and also includes the points and , so there are two valid alternative names, $\overrightarrow{GE}$ and $\overrightarrow{GO}$ , among the choices. The correct response is $\overrightarrow{GE}$ .

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Example Question #23 : Lines

Thingy

In the above diagram, let and be the midpoints of $\overline{OG}$ and $\overline{OE}$ , respectively, and and be the midpoints of $\overline{GK}$ and $\overline{OL}$ , respectively. Which of the following is not a valid alternative name for $\overrightarrow{RS}$ ?

Possible Answers:

Each of the other choices gives a valid alternative name for $\overrightarrow{RS}$ .

$\overrightarrow{RO}$

$\overrightarrow{RE}$

$\overrightarrow{RL}$

$\overrightarrow{RK}$

Correct answer:

Each of the other choices gives a valid alternative name for $\overrightarrow{RS}$ .

Explanation:

Below is the diagram with the points K,L,R , and , as described, shown in green. Also, $\overrightarrow{RS}$ , the ray that has endpoint and passes through , is marked in red.

Thingy_x

The ray also passes through E,K,L, and , so $\overrightarrow{RE}$ , $\overrightarrow{RK}$ , $\overrightarrow{RL}$ , and $\overrightarrow{RO}$ —all four given names—are also valid names for the ray.

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Example Question #411 : Geometry

What is the measure of an angle complementary to a $72 ^{\circ }$ angle?

Possible Answers:

$162 ^{\circ }$

$36 ^{\circ }$

$108 ^{\circ }$

$72 ^{\circ }$

$18 ^{\circ }$

Correct answer:

$18 ^{\circ }$

Explanation:

Complementary angles have degree measures that total $90 ^{\circ }$ , so the measure of an angle complementary to a $72 ^{\circ }$ angle would have measure $(90-72)^{\circ } = 18 ^{\circ }$ .

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Example Question #2 : Calculating An Angle Of A Line

What is the measure of an angle congruent to a $48 ^{\circ }$ angle?

Possible Answers:

$24 ^{\circ }$

$132 ^{\circ }$

$42 ^{\circ }$

$138^{\circ }$

$48 ^{\circ }$

Correct answer:

$48 ^{\circ }$

Explanation:

Two angles are congruent if they have the same degree measure, so an angle will be congruent to a $48 ^{\circ }$ angle if its measure is also $48 ^{\circ }$ .

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Example Question #1 : Calculating An Angle Of A Line

What is the measure of an angle supplementary to a $66 ^{\circ }$ angle?

Possible Answers:

$114 ^{\circ }$

$156 ^{\circ }$

$66 ^{\circ }$

$33 ^{\circ }$

$24 ^{\circ }$

Correct answer:

$114 ^{\circ }$

Explanation:

Supplementary angles have degree measures that total $180 ^{\circ }$ , so the measure of an angle complementary to a $66 ^{\circ }$ angle would have measure $\left ( 180- 66 \right )^{\circ } = 114^{\circ }$ .

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Example Question #412 : Geometry

What is the measure of an angle that is supplementary to a $68^{\circ}$ angle?

Possible Answers:

$292^{\circ}$

$22^{\circ}$

$68^{\circ}$

$86^{\circ}$

$112^{\circ}$

Correct answer:

$112^{\circ}$

Explanation:

Supplementary angles have degree measures that total $180^{\circ}$ , so an angle supplementary to $68^{\circ}$ would measure $180^{\circ}-68^{\circ}=112^{\circ}$ .

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GMAT Math : Geometry

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #9 : Understanding Rays

Example Question #10 : Understanding Rays

Example Question #21 : Lines

Example Question #22 : Lines

Example Question #653 : Problem Solving Questions

Example Question #23 : Lines

Example Question #411 : Geometry

Example Question #2 : Calculating An Angle Of A Line

Example Question #1 : Calculating An Angle Of A Line

Example Question #412 : Geometry

All GMAT Math Resources

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