How to find an angle in a right triangle - SSAT Upper Level Quantitative (Math)

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Question

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

Answer

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

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

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Question

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

Answer

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 $120^{\circ } > 90^{\circ }$ , it is obtuse. This makes it impossible for a right triangle to have a $120^{\circ }$ angle.

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Question

Find the degree measure of in the right triangle below.

Answer

The total number of degrees in a triangle is .

While $47^{\circ}$ 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 $90^{\circ}$ angle as well. To find the value of , subtract the other two degree measures from .

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

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Question

Find the angle value of .

Answer

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

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

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

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

$v=43^{\circ}$

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Question

Find the angle value of .

Answer

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

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

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

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

$w=58^{\circ}$

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Question

Find the angle value of .

Answer

All the angles in a triangle add up to degrees.

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

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

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

$y=46^{\circ}$

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Question

Find the angle measure of .

Answer

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

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

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

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

$z=31^{\circ}$

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