GMAT Math : Calculating an angle of a line

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Example Questions

Example Question #1 : Calculating An Angle Of A Line

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

Possible Answers:

$36 ^{\circ }$ $\displaystyle 36 ^{\circ }$

$18 ^{\circ }$ $\displaystyle 18 ^{\circ }$

$72 ^{\circ }$ $\displaystyle 72 ^{\circ }$

$162 ^{\circ }$ $\displaystyle 162 ^{\circ }$

$108 ^{\circ }$ $\displaystyle 108 ^{\circ }$

Correct answer:

$18 ^{\circ }$ $\displaystyle 18 ^{\circ }$

Explanation:

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

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Example Question #31 : Lines

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

Possible Answers:

$132 ^{\circ }$ $\displaystyle 132 ^{\circ }$

$42 ^{\circ }$ $\displaystyle 42 ^{\circ }$

$138^{\circ }$ $\displaystyle 138^{\circ }$

$24 ^{\circ }$ $\displaystyle 24 ^{\circ }$

$48 ^{\circ }$ $\displaystyle 48 ^{\circ }$

Correct answer:

$48 ^{\circ }$ $\displaystyle 48 ^{\circ }$

Explanation:

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

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Example Question #1 : Calculating An Angle Of A Line

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

Possible Answers:

$33 ^{\circ }$ $\displaystyle 33 ^{\circ }$

$24 ^{\circ }$ $\displaystyle 24 ^{\circ }$

$114 ^{\circ }$ $\displaystyle 114 ^{\circ }$

$156 ^{\circ }$ $\displaystyle 156 ^{\circ }$

$66 ^{\circ }$ $\displaystyle 66 ^{\circ }$

Correct answer:

$114 ^{\circ }$ $\displaystyle 114 ^{\circ }$

Explanation:

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

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Example Question #4 : Calculating An Angle Of A Line

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

Possible Answers:

$68^{\circ}$ $\displaystyle 68^{\circ}$

$112^{\circ}$ $\displaystyle 112^{\circ}$

$292^{\circ}$ $\displaystyle 292^{\circ}$

$86^{\circ}$ $\displaystyle 86^{\circ}$

$22^{\circ}$ $\displaystyle 22^{\circ}$

Correct answer:

$112^{\circ}$ $\displaystyle 112^{\circ}$

Explanation:

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

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Example Question #32 : Lines

What is the measure of an angle congruent to a $58^{\circ}$ $\displaystyle 58^{\circ}$ angle?

Possible Answers:

$302^{\circ}$ $\displaystyle 302^{\circ}$

$90^{\circ}$ $\displaystyle 90^{\circ}$

$58^{\circ}$ $\displaystyle 58^{\circ}$

$32^{\circ}$ $\displaystyle 32^{\circ}$

$122^{\circ}$ $\displaystyle 122^{\circ}$

Correct answer:

$58^{\circ}$ $\displaystyle 58^{\circ}$

Explanation:

Congruent angles have degree measures that are equal, so an angle congruent to $58^{\circ}$ $\displaystyle 58^{\circ}$ is $58^{\circ}$ $\displaystyle 58^{\circ}$.

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Example Question #6 : Calculating An Angle Of A Line

What is the measure of an angle that is complementary to a $42^{\circ }$ $\displaystyle 42^{\circ }$ angle?

Possible Answers:

$138^{\circ }$ $\displaystyle 138^{\circ }$

$90^{\circ }$ $\displaystyle 90^{\circ }$

$24^{\circ }$ $\displaystyle 24^{\circ }$

$48^{\circ }$ $\displaystyle 48^{\circ }$

$318^{\circ }$ $\displaystyle 318^{\circ }$

Correct answer:

$48^{\circ }$ $\displaystyle 48^{\circ }$

Explanation:

Complementary angles have degree measures that total $90^{\circ}$ $\displaystyle 90^{\circ}$, so an angle complementary to $42^{\circ}$ $\displaystyle 42^{\circ}$ would measure $90^{\circ}-42^{\circ}=48^{\circ}$ $\displaystyle 90^{\circ}-42^{\circ}=48^{\circ}$.

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Example Question #7 : Calculating An Angle Of A Line

What is the measure of an angle that is supplementary to a $80^{\circ}$ $\displaystyle 80^{\circ}$ angle?

Possible Answers:

$80^{\circ}$ $\displaystyle 80^{\circ}$

$20^{\circ}$ $\displaystyle 20^{\circ}$

$100^{\circ}$ $\displaystyle 100^{\circ}$

$10^{\circ}$ $\displaystyle 10^{\circ}$

$280^{\circ}$ $\displaystyle 280^{\circ}$

Correct answer:

$100^{\circ}$ $\displaystyle 100^{\circ}$

Explanation:

Supplementary angles have degree measures that total $180^{\circ }$ $\displaystyle 180^{\circ }$. Since we have an $80^{\circ}$ $\displaystyle 80^{\circ}$ angle, the supplementary angle would measure $180^{\circ}-80^{\circ }=100^{\circ}$ $\displaystyle 180^{\circ}-80^{\circ }=100^{\circ}$

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Example Question #8 : Calculating An Angle Of A Line

Which of the following angles is complementary to an $18^{\circ}$ $\displaystyle 18^{\circ}$ angle?

Possible Answers:

$342^{\circ}$ $\displaystyle 342^{\circ}$

$18^{\circ}$ $\displaystyle 18^{\circ}$

$72^{\circ}$ $\displaystyle 72^{\circ}$

$162^{\circ}$ $\displaystyle 162^{\circ}$

Not enough information provided.

Correct answer:

$72^{\circ}$ $\displaystyle 72^{\circ}$

Explanation:

Complementary angles have degree measures that total $90^{\circ }$ $\displaystyle 90^{\circ }$. Since we have an $18^{\circ}$ $\displaystyle 18^{\circ}$ angle, the supplementary angle would measure $90^{\circ}-18^{\circ }=72^{\circ}$ $\displaystyle 90^{\circ}-18^{\circ }=72^{\circ}$

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Example Question #33 : Lines

Which of the following angles is congruent to a $119^{\circ}$ $\displaystyle 119^{\circ}$ angle?

Possible Answers:

$249^{\circ}$ $\displaystyle 249^{\circ}$

$71^{\circ}$ $\displaystyle 71^{\circ}$

$-29^{\circ}$ $\displaystyle -29^{\circ}$

$119^{\circ}$ $\displaystyle 119^{\circ}$

Not enough information to solve.

Correct answer:

$119^{\circ}$ $\displaystyle 119^{\circ}$

Explanation:

Congruent angles have the same degree measure, so an angle congruent to a $119^{\circ}$ $\displaystyle 119^{\circ}$ angle would also measure $119^{\circ}$ $\displaystyle 119^{\circ}$.

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Example Question #10 : Calculating An Angle Of A Line

What is the measurement of an angle that is supplementary to a $16^{\circ}$ $\displaystyle 16^{\circ}$ angle?

Possible Answers:

$16^{\circ}$ $\displaystyle 16^{\circ}$

$180^{\circ}$ $\displaystyle 180^{\circ}$

$90^{\circ}$ $\displaystyle 90^{\circ}$

$164^{\circ}$ $\displaystyle 164^{\circ}$

$74^{\circ}$ $\displaystyle 74^{\circ}$

Correct answer:

$164^{\circ}$ $\displaystyle 164^{\circ}$

Explanation:

Two angles are supplementary if the total of their degree measures is $180^{\circ }$ $\displaystyle 180^{\circ }$. Therefore, an angle supplementary to a $16^{\circ}$ $\displaystyle 16^{\circ}$ angle measures $180^{\circ }-16^{\circ}=164^{\circ}$ $\displaystyle 180^{\circ }-16^{\circ}=164^{\circ}$.

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GMAT Math : Calculating an angle of a line

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #1 : Calculating An Angle Of A Line

Example Question #31 : Lines

Example Question #1 : Calculating An Angle Of A Line

Example Question #4 : Calculating An Angle Of A Line

Example Question #32 : Lines

Example Question #6 : Calculating An Angle Of A Line

Example Question #7 : Calculating An Angle Of A Line

Example Question #8 : Calculating An Angle Of A Line

Example Question #33 : Lines

Example Question #10 : Calculating An Angle Of A Line

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