GMAT Math : Calculating an angle of a line

Study concepts, example questions & explanations for GMAT Math

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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 \(\displaystyle 72 ^{\circ }\) angle?

Possible Answers:

\(\displaystyle 36 ^{\circ }\)

\(\displaystyle 18 ^{\circ }\)

\(\displaystyle 72 ^{\circ }\)

\(\displaystyle 162 ^{\circ }\)

\(\displaystyle 108 ^{\circ }\)

Correct answer:

\(\displaystyle 18 ^{\circ }\)

Explanation:

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

Example Question #31 : Lines

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

Possible Answers:

\(\displaystyle 132 ^{\circ }\)

\(\displaystyle 42 ^{\circ }\)

\(\displaystyle 138^{\circ }\)

\(\displaystyle 24 ^{\circ }\)

\(\displaystyle 48 ^{\circ }\)

Correct answer:

\(\displaystyle 48 ^{\circ }\)

Explanation:

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

Example Question #1 : Calculating An Angle Of A Line

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

Possible Answers:

\(\displaystyle 33 ^{\circ }\)

\(\displaystyle 24 ^{\circ }\)

\(\displaystyle 114 ^{\circ }\)

\(\displaystyle 156 ^{\circ }\)

\(\displaystyle 66 ^{\circ }\)

Correct answer:

\(\displaystyle 114 ^{\circ }\)

Explanation:

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

Example Question #4 : Calculating An Angle Of A Line

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

Possible Answers:

\(\displaystyle 68^{\circ}\)

\(\displaystyle 112^{\circ}\)

\(\displaystyle 292^{\circ}\)

\(\displaystyle 86^{\circ}\)

\(\displaystyle 22^{\circ}\)

Correct answer:

\(\displaystyle 112^{\circ}\)

Explanation:

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

Example Question #32 : Lines

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

Possible Answers:

\(\displaystyle 302^{\circ}\)

\(\displaystyle 90^{\circ}\)

\(\displaystyle 58^{\circ}\)

\(\displaystyle 32^{\circ}\)

\(\displaystyle 122^{\circ}\)

Correct answer:

\(\displaystyle 58^{\circ}\)

Explanation:

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

Example Question #6 : Calculating An Angle Of A Line

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

Possible Answers:

\(\displaystyle 138^{\circ }\)

\(\displaystyle 90^{\circ }\)

\(\displaystyle 24^{\circ }\)

\(\displaystyle 48^{\circ }\)

\(\displaystyle 318^{\circ }\)

Correct answer:

\(\displaystyle 48^{\circ }\)

Explanation:

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

Example Question #7 : Calculating An Angle Of A Line

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

Possible Answers:

\(\displaystyle 80^{\circ}\)

\(\displaystyle 20^{\circ}\)

\(\displaystyle 100^{\circ}\)

\(\displaystyle 10^{\circ}\)

\(\displaystyle 280^{\circ}\)

Correct answer:

\(\displaystyle 100^{\circ}\)

Explanation:

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

Example Question #8 : Calculating An Angle Of A Line

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

Possible Answers:

\(\displaystyle 342^{\circ}\)

\(\displaystyle 18^{\circ}\)

\(\displaystyle 72^{\circ}\)

\(\displaystyle 162^{\circ}\)

Not enough information provided.

Correct answer:

\(\displaystyle 72^{\circ}\)

Explanation:

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

Example Question #33 : Lines

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

Possible Answers:

\(\displaystyle 249^{\circ}\)

\(\displaystyle 71^{\circ}\)

\(\displaystyle -29^{\circ}\)

\(\displaystyle 119^{\circ}\)

Not enough information to solve.

Correct answer:

\(\displaystyle 119^{\circ}\)

Explanation:

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

Example Question #10 : Calculating An Angle Of A Line

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

Possible Answers:

\(\displaystyle 16^{\circ}\)

\(\displaystyle 180^{\circ}\)

\(\displaystyle 90^{\circ}\)

\(\displaystyle 164^{\circ}\)

\(\displaystyle 74^{\circ}\)

Correct answer:

\(\displaystyle 164^{\circ}\)

Explanation:

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

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