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HSPT Math : HSPT Mathematics

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Example Questions

Example Question #1452 : Concepts

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:

$68^{\circ }$

$56^{\circ }$

$62^{\circ }$

$73^{\circ }$

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 #1453 : Concepts

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:

$134^{\circ }$

$136^{\circ }$

$89^{\circ }$

$46^{\circ }$

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 #1454 : Concepts

In parallelogram ABCD ,

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

and

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

Express in terms of .

Possible Answers:

Y = X+ 45

Y = 67- X

Y = 157- X

Y = X+ 23

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 #272 : Geometry

In parallelogram ABCD ,

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

and

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

Express in terms of .

Possible Answers:

Y = X+ 45

Y = 67- X

Y = 157- 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 #273 : 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:

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

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

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

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

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 #1461 : Concepts

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

Possible Answers:

$37^{\circ }$

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

$43 ^{\circ }$

$47^{\circ }$

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 #1462 : Concepts

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

Possible Answers:

$48^{\circ }$

$156 ^{\circ }$

$114 ^{\circ }$

$66 ^{\circ }$

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 #275 : 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 acute triangle.

$\bigtriangleup DEF$ is a right triangle.

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

$\bigtriangleup DEF$ is an obtuse triangle.

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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Example Question #1465 : Concepts

$\bigtriangleup ABC \sim \bigtriangleup DEF$ .

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

Is $\bigtriangleup DEF$ scalene, isosceles, or equilateral - or can it be determined?

Possible Answers:

$\bigtriangleup DEF$ is a scalene triangle.

$\bigtriangleup DEF$ is a isosceles triangle, but not equilateral.

$\bigtriangleup DEF$ is an equilateral triangle.

Whether $\bigtriangleup DEF$ is scalene, isosceles, or equilateral cannot be determined.

Correct answer:

$\bigtriangleup DEF$ is an equilateral 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

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

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

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

The three angles of $\bigtriangleup DEF$ all measure the same, so it is equiangular; consequently, it is also equilateral.

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Example Question #281 : Geometry

In parallelogram ABCD , $m \angle A = (t+ 56 )^{\circ }$ . Give the measure of $\angle C$ in terms of .

Possible Answers:

$(t+ 146)^{\circ }$

$(124-t )^{\circ }$

$(t+ 56 )^{\circ }$

$(34-t )^{\circ }$

Correct answer:

$(t+ 56 )^{\circ }$

Explanation:

$\angle A$ and $\angle C$ are a pair of opposite angles of the parallelogram, and as such, they are congruent. Therefore,

$m \angle C = m \angle A = (t+ 56 )^{\circ }$ .

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HSPT Math : HSPT Mathematics

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #1452 : Concepts

Example Question #1453 : Concepts

Example Question #1454 : Concepts

Example Question #272 : Geometry

Example Question #273 : Geometry

Example Question #1461 : Concepts

Example Question #1462 : Concepts

Example Question #275 : Geometry

Example Question #1465 : Concepts

Example Question #281 : Geometry

All HSPT Math Resources

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