Calculating an angle of a line

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GMAT Quantitative › Calculating an angle of a line

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What is the measure of an angle that is complementary to a $70^{\circ}$ angle?

$20^{\circ}$

CORRECT

$70^{\circ}$

$110^{\circ}$

$290^{\circ}$

$90^{\circ}$

Explanation

Two angles are complementary if the total of their degree measures is $90^{\circ }$ . Therefore, an angle complementary to a $70^{\circ}$ angle measures $90^{\circ }-70^{\circ}=20^{\circ}$ .

What is the measurement of an angle that is congruent to an $89^{\circ }$ angle?

$89^{\circ }$

CORRECT

$1^{\circ }$

$91^{\circ }$

$271^{\circ }$

$90^{\circ }$

Explanation

Two angles are congruent if they have the same degree measure. Therefore, an angle congruent to an $89^{\circ }$ angle also measures $89^{\circ }$ .

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

$114 ^{\circ }$

CORRECT

$24 ^{\circ }$

$66 ^{\circ }$

$33 ^{\circ }$

$156 ^{\circ }$

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 $\left ( 180- 66 \right )^{\circ } = 114^{\circ }$ .

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

$164^{\circ}$

CORRECT

$74^{\circ}$

$16^{\circ}$

$90^{\circ}$

$180^{\circ}$

Explanation

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

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

$48 ^{\circ }$

CORRECT

$42 ^{\circ }$

$132 ^{\circ }$

$24 ^{\circ }$

$138^{\circ }$

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 $48 ^{\circ }$ .

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

$112^{\circ}$

CORRECT

$22^{\circ}$

$68^{\circ}$

$86^{\circ}$

$292^{\circ}$

Explanation

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

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

$100^{\circ}$

CORRECT

$10^{\circ}$

$280^{\circ}$

$20^{\circ}$

$80^{\circ}$

Explanation

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

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

$18 ^{\circ }$

CORRECT

$72 ^{\circ }$

$108 ^{\circ }$

$36 ^{\circ }$

$162 ^{\circ }$

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 $(90-72)^{\circ } = 18 ^{\circ }$ .

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

$72^{\circ}$

CORRECT

$18^{\circ}$

$162^{\circ}$

$342^{\circ}$

Not enough information provided.

Explanation

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

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

$48^{\circ }$

CORRECT

$138^{\circ }$

$24^{\circ }$

$90^{\circ }$

$318^{\circ }$

Explanation

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

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