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HSPT Math : Concepts

Study concepts, example questions & explanations for HSPT Math

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Example Questions

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Example Question #261 : Geometry

The three angles of a triangle are labeled , , and . If is $97^{\circ}$ , what is the value of X+Y ?

Possible Answers:

$83^{\circ}$

$73^{\circ}$

$93^{\circ}$

$17^{\circ}$

Correct answer:

$83^{\circ}$

Explanation:

Given that the three angles of a triangle always add up to 180 degrees, the following equation can be used:

X+Y+Z=180

X+Y+97=180

X+Y=83

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Example Question #262 : Geometry

An isosceles triangle has a vertex angle of seventy degrees. What is the angle of one of the other angles?

Possible Answers:

110

Correct answer:

Explanation:

A triangle has three sides and three angles, which add up to 180 degrees.

An isosceles triangle must have 2 equal sides and 2 equal base angles. Given the vertex angle is 70 degrees, subtract this angle by 180.

180-70=110

Since the other 2 base angles must equal to each other in an isoceles triangle, divide 110 with 2 to get the measure of the other angles.

$\frac{110}{2}=55$

The base angles must be degrees each.

As a check:

$55+55+70=180 \textup{ degrees}$

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Example Question #261 : Geometry

What is the measure of an interior angle of a regular pentagon?

Possible Answers:

116

112

124

108

Correct answer:

108

Explanation:

The formula to find the sum of total interior angles of a polygon is:

$(n-2)\times 180$

Since there are five sides in the pentagon, substitute n=5 .

$(5-2)\times 180=540$

This is the sum of the interior angles of a pentagon. To find an interior angle, divide by five since there are five interior angles in a pentagon.

$\frac{540}{5}= 108$

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Example Question #11 : How To Find An Angle Of A Line

$\dpi{100} \small \overline{AB}$ is a straight line. $\dpi{100} \small \overline{CD}$ intersects $\dpi{100} \small \overline{AB}$ at point $\dpi{100} \small E$ . If $\dpi{100} \small \angle AEC$ measures 120 degrees, what must be the measure of $\dpi{100} \small \angle BEC$ ?

Possible Answers:

$\dpi{100} \small 75$ degrees

$\dpi{100} \small 70$ degrees

None of the other answers

$\dpi{100} \small 60$ degrees

$\dpi{100} \small 65$ degrees

Correct answer:

$\dpi{100} \small 60$ degrees

Explanation:

$\dpi{100} \small \angle AEC$ & $\dpi{100} \small \angle BEC$ must add up to 180 degrees. So, if $\dpi{100} \small \angle AEC$ is 120, $\dpi{100} \small \angle BEC$ (the supplementary angle) must equal 60, for a total of 180.

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Example Question #1451 : Concepts

Find the total interior degrees in an octagon.

Possible Answers:

2160

900

360

1080

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 #272 : Geometry

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:

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

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

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

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

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

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 #273 : 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:

$62^{\circ }$

$56^{\circ }$

$68^{\circ }$

$73^{\circ }$

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 #2051 : Hspt Mathematics

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:

$46^{\circ }$

$89^{\circ }$

$134^{\circ }$

$136^{\circ }$

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 #1451 : 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+ 23

Y = 67- X

Y = 157- X

Y = X+ 45

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 #276 : Geometry

In parallelogram ABCD ,

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

and

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

Express in terms of .

Possible Answers:

Y = 67- X

Y = X+ 45

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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HSPT Math : Concepts

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #261 : Geometry

Example Question #262 : Geometry

Example Question #261 : Geometry

Example Question #11 : How To Find An Angle Of A Line

Example Question #1451 : Concepts

Example Question #272 : Geometry

Example Question #273 : Geometry

Example Question #2051 : Hspt Mathematics

Example Question #1451 : Concepts

Example Question #276 : Geometry

All HSPT Math Resources

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