Calculating an angle of a line - GMAT Quantitative Reasoning

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Question

A right triangle is given with a missing value of . It is stated that the triangle is an acute right triangle with angles $50^\circ$ and . What is a possible value of in degrees?

Answer

It is important to recall that all triangles add to 180 degrees and a right triangle contains one angle that is equal to 90 degrees. Therefore, in this particular problem we can write the following equation to solve for the missing variable.

$\90^\circ+50^\circ+2t=180^\circ \140^\circ-2t=180^\circ \2t=180^\circ-140^\circ \2t=40^\circ \t=20$

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Question

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

Answer

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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Question

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

Answer

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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Question

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

Answer

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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Question

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

Answer

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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Question

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

Answer

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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Question

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

Answer

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

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Question

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

Answer

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

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Question

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

Answer

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

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Question

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

Answer

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

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Question

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

Answer

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

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Question

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

Answer

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

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Question

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

Answer

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

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