SSAT Upper Level Math : How to find an angle in a right triangle

Study concepts, example questions & explanations for SSAT Upper Level Math

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Example Questions

Example Question #1 : How To Find An Angle In A Right Triangle

One angle of a right triangle has measure \displaystyle 120^{\circ }. Give the measures of the other two angles.

Possible Answers:

\displaystyle 90^{\circ }, 120^{\circ }

\displaystyle 30^{\circ }, 90^{\circ }

\displaystyle 30^{\circ }, 30^{\circ }

This triangle cannot exist.

\displaystyle 120^{\circ }, 120^{\circ }

Correct answer:

This triangle cannot exist.

Explanation:

A right triangle must have one right angle and two acute angles; this means that no angle of a right triangle can be obtuse. But since \displaystyle 120^{\circ } > 90^{\circ }, it is obtuse. This makes it impossible for a right triangle to have a \displaystyle 120^{\circ } angle.

Example Question #1 : How To Find An Angle In A Right Triangle

One angle of a right triangle has measure \displaystyle 68^{\circ }. Give the measures of the other two angles.

Possible Answers:

\displaystyle 44^{\circ },68^{\circ }

\displaystyle 56^{\circ },56^{\circ }

\displaystyle 22^{\circ }, 90^{\circ }

\displaystyle 52^{\circ }, 60^{\circ }

This triangle cannot exist.

Correct answer:

\displaystyle 22^{\circ }, 90^{\circ }

Explanation:

One of the angles of a right triangle is by definition a right, or \displaystyle 90^{\circ }, angle, so this is the measure of one of the missing angles. Since the measures of the angles of a triangle total \displaystyle 180^{\circ }, if we let the measure of the third angle be \displaystyle x, then:

\displaystyle x + 68 + 90 = 180

\displaystyle x + 158 = 180

\displaystyle x + 158 - 158= 180 - 158

\displaystyle x = 22

The other two angles measure \displaystyle 22 ^{\circ }, 90^{\circ }.

Example Question #2 : How To Find An Angle In A Right Triangle

Find the degree measure of \displaystyle x in the right triangle below.

 

Picture1

Possible Answers:

\displaystyle 47^{\circ}

\displaystyle 90^{\circ}

\displaystyle 32^{\circ}

\displaystyle 43^{\circ}

Correct answer:

\displaystyle 43^{\circ}

Explanation:

The total number of degrees in a triangle is \displaystyle 180.

While \displaystyle 47^{\circ} is provided as the measure of one of the angles in the diagram, you are also told that the triangle is a right triangle, meaning that it must contain a \displaystyle 90^{\circ} angle as well. To find the value of \displaystyle x, subtract the other two degree measures from \displaystyle 180.

\displaystyle x=180-90-47=43^{\circ}

Example Question #51 : Properties Of Triangles

Find the angle value of \displaystyle v.

Picture1

Possible Answers:

\displaystyle 47^{\circ}

\displaystyle 43^{\circ}

\displaystyle 53^{\circ}

\displaystyle 90^{\circ}

Correct answer:

\displaystyle 43^{\circ}

Explanation:

All the angles in a triangle must add up to 180 degrees.

\displaystyle 90^{\circ}+47^{\circ}+v=180^{\circ}

\displaystyle 137^{\circ}+v=180^{\circ}

\displaystyle 137^{\circ}+v-137^{\circ}=180^{\circ}-137^{\circ}

\displaystyle v=43^{\circ}

Example Question #5 : How To Find An Angle In A Right Triangle

Find the angle value of \displaystyle w.

Picture1

Possible Answers:

\displaystyle 48^{\circ}

\displaystyle 68^{\circ}

\displaystyle 38^{\circ}

\displaystyle 58^{\circ}

Correct answer:

\displaystyle 58^{\circ}

Explanation:

All the angles in a triangle adds up to \displaystyle 180^{\circ}.

\displaystyle 90^{\circ}+32^{\circ}+w=180^{\circ}

\displaystyle 122^{\circ}+w=180^{\circ}

\displaystyle 122^{\circ}+w-122^{\circ}=180^{\circ}-122^{\circ}

\displaystyle w=58^{\circ}

Example Question #6 : How To Find An Angle In A Right Triangle

Find the angle value of \displaystyle y.

Picture1

Possible Answers:

\displaystyle 36^{\circ}

\displaystyle 66^{\circ}

\displaystyle 46^{\circ}

\displaystyle 56^{\circ}

Correct answer:

\displaystyle 46^{\circ}

Explanation:

All the angles in a triangle add up to \displaystyle 180 degrees.

\displaystyle 90^{\circ}+44^{\circ}+y=180^{\circ}

\displaystyle 134^{\circ}+y=180^{\circ}

\displaystyle 134^{\circ}+y-134^{\circ}=180^{\circ}-134^{\circ}

\displaystyle y=46^{\circ}

Example Question #52 : Right Triangles

Find the angle measure of \displaystyle z.

Picture1

Possible Answers:

\displaystyle 41^{\circ}

\displaystyle 31^{\circ}

\displaystyle 51^{\circ}

\displaystyle 21^{\circ}

Correct answer:

\displaystyle 31^{\circ}

Explanation:

All the angles in a triangle add up to \displaystyle 180^{\circ}.

\displaystyle 90^{\circ}+59^{\circ}+z=180^{\circ}

\displaystyle 149^{\circ}+z=180^{\circ}

\displaystyle 149^{\circ}+z-149^{\circ}=180^{\circ}-149^{\circ}

\displaystyle z=31^{\circ}

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