GMAT Math : Calculating an angle of a line

Study concepts, example questions & explanations for GMAT Math

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Example Questions

Example Question #424 : Geometry

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

Possible Answers:

\(\displaystyle 70^{\circ}\)

\(\displaystyle 290^{\circ}\)

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

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

\(\displaystyle 110^{\circ}\)

Correct answer:

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

Explanation:

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

Example Question #661 : Problem Solving Questions

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

Possible Answers:

\(\displaystyle 91^{\circ }\)

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

\(\displaystyle 271^{\circ }\)

\(\displaystyle 89^{\circ }\)

\(\displaystyle 1^{\circ }\)

Correct answer:

\(\displaystyle 89^{\circ }\)

Explanation:

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

Example Question #662 : Problem Solving Questions

A right triangle is given with a missing value of \(\displaystyle t\). It is stated that the triangle is an acute right triangle with angles \(\displaystyle 50^\circ\) and \(\displaystyle 2t\). What is a possible value of \(\displaystyle t\) in degrees?

Possible Answers:

\(\displaystyle 40\)

Cannot be determined

\(\displaystyle 80\)

\(\displaystyle 60\)

\(\displaystyle 20\)

Correct answer:

\(\displaystyle 20\)

Explanation:

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.

\(\displaystyle \\90^\circ+50^\circ+2t=180^\circ \\140^\circ-2t=180^\circ \\2t=180^\circ-140^\circ \\2t=40^\circ \\t=20\)

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