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HSPT Math : Geometry

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Example Questions

Example Question #271 : Geometry

Find the total interior degrees in an octagon.

Possible Answers:

2160

360

1080

900

Correct answer:

1080

Explanation:

To solve, simply use the formula for the total of the interior angles where n is the number of vertices.

In this particular case n=8 .

Thus,

degrees=(n-2)*180=(8-2)*180=6*180=1080

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Example Question #1453 : Concepts

Two angles are supplementary. The measure of one angle is 23 degrees less than twice that of the second. Give the lesser of the measures of the two angles.

Possible Answers:

$112 \frac{1}{3}^{\circ }$

$78 \frac{1}{2}^{\circ }$

$12\frac{5}{9}^{\circ }$

$77\frac{4}{9}^{\circ }$

$67 \frac{2}{3} ^{\circ }$

Correct answer:

$67 \frac{2}{3} ^{\circ }$

Explanation:

Let be the measure of one of the angles. The measure of the other angle is 23 degrees less than twice this, which is 2X - 23 . The angles are supplementary, meaning that their measures add up to 180. Therefore:

(2X - 23) + X = 180

3X - 23 = 180

3X - 23+ 23 = 180 + 23

3X = 203

$3X\div 3 = 203 \div 3$

$X = 67 \frac{2}{3}$

The other angle has measure $180 - 67 \frac{2}{3} = 112 \frac{1}{3}$ .

The lesser of the two measures is requested, so the correct response is $67 \frac{2}{3} ^{\circ }$ .

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Example Question #272 : Geometry

An angle of measure $X ^{\circ }$ is supplementary to an angle of measure $124 ^{\circ }$ .

An angle of measure $2 X ^{\circ }$ is supplementary to an angle of what measure?

Possible Answers:

$56^{\circ }$

$68^{\circ }$

$73^{\circ }$

$62^{\circ }$

Correct answer:

$68^{\circ }$

Explanation:

Two angles are supplementary if the sum of their degree measures is 180.

An angle supplementary to an angle of measure $124 ^{\circ }$ has measure

$180 ^{\circ }- 124 ^{\circ } = 56 ^{\circ }$ ,

so X = 56 , and $2X = 2 \cdot 56 = 112$ .

An angle of measure $112^{\circ }$ is supplementary to an angle of measure

$180 ^{\circ }- 112 ^{\circ } = 68 ^{\circ }$ ,

the correct choice.

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Example Question #273 : Geometry

An angle of measure $X ^{\circ }$ is supplementary to an angle of measure $88 ^{\circ }$ .

An angle of measure $\frac{1}{2}X ^{\circ }$ is supplementary to an angle of what measure?

Possible Answers:

$134^{\circ }$

$89^{\circ }$

$46^{\circ }$

$136^{\circ }$

Correct answer:

$134^{\circ }$

Explanation:

Two angles are supplementary if the sum of their degree measures is 180.

An angle supplementary to an angle of measure $88 ^{\circ }$ has measure

$180 ^{\circ }- 88 ^{\circ } = 92^{\circ }$ ,

so X = 92 , and $\frac{1}{2}X = \frac{1}{2} \cdot 92 = 46$ .

An angle of measure $46^{\circ }$ is supplementary to an angle of measure

$180 ^{\circ }- 46 ^{\circ } = 134^{\circ }$ ,

the correct choice.

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Example Question #274 : Geometry

In parallelogram ABCD ,

$m \angle A =( X+ 34) ^{\circ }$

and

$m \angle B =( Y - 11) ^{\circ }$

Express in terms of .

Possible Answers:

Y = 157- X

Y = X+ 45

Y = X+ 23

Y = 67- X

Correct answer:

Y = 157- X

Explanation:

$\angle A$ and $\angle B$ , as adjacent angles of a parallelogram, have degree measures totaling $180 ^{\circ }$ , so

$m \angle A+ m \angle B = 180^{\circ }$

(X+34)+ (Y-11) = 180

X+34+ Y-11= 180

X+ Y+34-11= 180

X+ Y+23= 180

X+ Y+23 - 23 - X = 180 - 23 - X

Y = 157- X

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Example Question #275 : Geometry

In parallelogram ABCD ,

$m \angle A =( X+ 34) ^{\circ }$

and

$m \angle C =( Y - 11) ^{\circ }$

Express in terms of .

Possible Answers:

Y = 157- X

Y = X+ 45

Y = 67- X

Y = X+ 23

Correct answer:

Y = X+ 45

Explanation:

$\angle A$ and $\angle C$ , as adjacent angles of a parallelogram, have the same degree measure, so

$m \angle C =m \angle A$

Y - 11 = X + 34

Y - 11 + 11 = X + 34 + 11

Y = X+ 45

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Example Question #276 : Geometry

Two angles are complementary. The measure of one angle is 23 degrees less than twice that of the second. Give the greater of the measures of the two angles.

Possible Answers:

$67 \frac{2}{3} ^{\circ }$

$52 \frac{1}{3} ^{\circ }$

$37 \frac{2}{3}^{\circ }$

$78 \frac{1}{2}^{\circ }$

Correct answer:

$52 \frac{1}{3} ^{\circ }$

Explanation:

Let be the measure of one of the angles. The measure of the other angle is 23 degrees less than twice this, which is 2X - 23 . The angles are complementary, meaning that their measures add up to 90. Therefore:

(2X - 23) + X = 90

3X - 23 = 90

3X - 23+ 23 = 90 + 23

3X = 113

$3X\div 3 = 113 \div 3$

$X = 37 \frac{2}{3}$

The other angle has measure $90- 37 \frac{2}{3} = 52 \frac{1}{3}$ .

The greater of the two measures is requested, so the correct response is $52 \frac{1}{3} ^{\circ }$ .

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Example Question #277 : Geometry

An angle supplementary to an angle of measure $137^{\circ }$ is complementary to an angle of what measure?

Possible Answers:

$43 ^{\circ }$

$68 \frac{1}{2} ^{\circ }$

$37^{\circ }$

$47^{\circ }$

Correct answer:

$47^{\circ }$

Explanation:

Two angles are supplementary if the sum of their degree measures is 180; Two angles are complementary if the sum of their degree measures is 90.

An angle supplementary to an angle with measure $137^{\circ }$ has measure

$180 ^{\circ } - 137^{\circ } = 43^{\circ }$ ;

this is complementary to an angle with measure

$90 ^{\circ } - 43^{\circ } = 47 ^{\circ }$ .

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Example Question #278 : Geometry

An angle complementary to an angle of measure $24^{\circ }$ is supplementary to an angle of what measure?

Possible Answers:

$156 ^{\circ }$

$48^{\circ }$

$114 ^{\circ }$

$66 ^{\circ }$

Correct answer:

$114 ^{\circ }$

Explanation:

Two angles are supplementary if the sum of their degree measures is 180; Two angles are scomplementary if the sum of their degree measures is 90.

An angle complementary to an angle with measure $24^{\circ }$ has measure

$90 ^{\circ } - 24 ^{\circ } = 66 ^{\circ }$ ;

this is supplementary to an angle with measure

$180 ^{\circ } - 66 ^{\circ } = 114^{\circ }$ .

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Example Question #279 : Geometry

$\bigtriangleup ABC \sim \bigtriangleup DEF$ .

$m \angle A = m \angle C = 60 ^{\circ }$ .

Is $\bigtriangleup DEF$ acute, right, or obtuse - or can it be determined?

Possible Answers:

$\bigtriangleup DEF$ is an obtuse triangle.

$\bigtriangleup DEF$ is a right triangle.

$\bigtriangleup DEF$ is an acute triangle.

Whether $\bigtriangleup DEF$ is acute, right, or obtuse cannot be determined.

Correct answer:

$\bigtriangleup DEF$ is an acute triangle.

Explanation:

Corresponding angles of similar triangles are congruent, so

$m \angle D = m \angle A = 60^{\circ }$

$m \angle F = m \angle C = 60^{\circ }$

The degree measures of the angles of a triangle total 180, so

$m \angle E =180^{\circ } - (m \angle D +m \angle F )$

$m \angle E =180^{\circ } - (60^{\circ } +60^{\circ } )$

$m \angle E =60^{\circ }$

All three angles of $\bigtriangleup DEF$ are acute, measuring less than 90 degrees, so $\bigtriangleup DEF$ is acute.

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HSPT Math : Geometry

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #271 : Geometry

Example Question #1453 : Concepts

Example Question #272 : Geometry

Example Question #273 : Geometry

Example Question #274 : Geometry

Example Question #275 : Geometry

Example Question #276 : Geometry

Example Question #277 : Geometry

Example Question #278 : Geometry

Example Question #279 : Geometry

All HSPT Math Resources

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