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HSPT Math : HSPT Mathematics

Study concepts, example questions & explanations for HSPT Math

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6 Diagnostic Tests 130 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1404 : Concepts

What is the measure of a right angle?

Possible Answers:

180

360

Correct answer:

Explanation:

The measure of a right angle is degrees.

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Example Question #1402 : Concepts

Triangle_a

Figure NOT drawn to scale.

If $w = 125^{\circ }$ and $x = 81^{\circ }$ , evaluate .

Possible Answers:

More information is needed to solve the problem.

$35^{\circ}$

$53^{\circ }$

$44^{\circ }$

$55^{\circ }$

Correct answer:

$44^{\circ }$

Explanation:

The measure of an exterior angle of a triangle is the sum of the measures of its remote interior angles, so

w = x + y

$y = w - x= 125 - 81 = 44^{\circ }$

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Example Question #1403 : Concepts

Triangle_a

Figure NOT drawn to scale.

If $x = 72^{\circ }$ and $y = 43^{\circ }$ , evaluate .

Possible Answers:

$137^{\circ}$

$115^{\circ }$

$125^{\circ }$

$108^{\circ}$

$65^{\circ}$

Correct answer:

$115^{\circ }$

Explanation:

The measure of an exterior angle of a triangle is the sum of the measures of its remote interior angles, so

$w = x + y = 72 + 43 = 115 ^{\circ }$

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Example Question #225 : Geometry

If the vertex angle of an isoceles triangle is $64^{\circ}$ , what is the value of one of its base angles?

Possible Answers:

$64^{\circ}$

$116^{\circ}$

$36^{\circ}$

$58^{\circ}$

$26^{\circ}$

Correct answer:

$58^{\circ}$

Explanation:

In an isosceles triangle, the base angles are the same. Also, the three angles of a triangle add up to $180^{\circ}$ .

So, subtract the vertex angle from $180^{\circ}$ . You get $116^{\circ}$ .

Because there are two base angles you divide $116^{\circ}$ by , and you get $58^{\circ}$ .

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Example Question #771 : Ssat Upper Level Quantitative (Math)

Triangle

Note: Figure NOT drawn to scale.

Refer to the above diagram.

$45^{\circ } \leq m \angle 1 \leq 50^{\circ }$

$60^{\circ } \leq m \angle 2 \leq 70 ^{\circ }$

Which of the following could be a measure of $\angle 3$ ?

Possible Answers:

$125^{\circ }$

All of the other choices give a possible measure of $\angle 3$ .

$100^{\circ }$

$110^{\circ }$

$130^{\circ }$

Correct answer:

$110^{\circ }$

Explanation:

The measure of an exterior angle of a triangle is the sum of the measures of its remote interior angles, so

$\angle 3 = \angle 1 + \angle 2$ .

We also have the following constraints:

$45^{\circ } \leq m \angle 1 \leq 50^{\circ }$

$60^{\circ } \leq m \angle 2 \leq 70 ^{\circ }$

Then, by the addition property of inequalities,

$45^{\circ } + 60 ^{\circ }\leq m \angle 1 +m \angle 2 \leq 50^{\circ } + 70 ^{\circ }$

$105 ^{\circ }\leq m \angle 3 \leq 120^{\circ }$

Therefore, the measure of $\angle 3$ must fall in that range. Of the given choices, only $110^{\circ }$ falls in that range.

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Example Question #1 : How To Find An Angle In An Acute / Obtuse Triangle

Triangle

Refer to the above diagram.

$45^{\circ } \leq m \angle 1 \leq 50^{\circ }$

$130^{\circ } \leq m \angle 3 \leq 140 ^{\circ }$

Which of the following could be a measure of $\angle 2$ ?

Possible Answers:

$80 ^{\circ }$

$95 ^{\circ }$

$85 ^{\circ }$

$90 ^{\circ }$

All of the other responses are correct.

Correct answer:

All of the other responses are correct.

Explanation:

The measure of an exterior angle of a triangle is the sum of the measures of its remote interior angles, so

$\angle 3 = \angle 1 + \angle 2$

$\angle 2 = \angle 3 - \angle 1$

Therefore, the maximum value of $\angle 2$ is the least possible value of $\angle 1$ subtracted from the greatest possible value of $\angle 3$ :

$140^{\circ } - 45^{\circ } = 95 ^{\circ }$

The minimum value of $\angle 2$ is the greatest possible value of $\angle 1$ subtracted from the least possible value of $\angle 3$ :

$130^{\circ } - 50^{\circ } = 80 ^{\circ }$

Therefore,

$80^{\circ } \leq \angle 2 \leq 95^{\circ }$

Since all of the choices fall in this range, all are possible measures of $\angle 2$ .

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

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

Possible Answers:

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

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

$30^{\circ }, 30^{\circ }$

This triangle cannot exist.

$120^{\circ }, 120^{\circ }$

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

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

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

Possible Answers:

This triangle cannot exist.

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

$56^{\circ },56^{\circ }$

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

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

Correct answer:

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

Explanation:

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:

x + 68 + 90 = 180

x + 158 = 180

x + 158 - 158= 180 - 158

x = 22

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

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Example Question #1 : How To Find An Angle Of A Line

Varsity_question

AB and CD are two parrellel lines intersected by line EF. If the measure of angle 1 is 132^o , what is the measure of angle 2?

Possible Answers:

$180^{\circ}$

$48^{\circ}$

$24^{\circ}$

$64^{\circ}$

$132^{\circ}$

Correct answer:

$132^{\circ}$

Explanation:

The angles are equal. When two parallel lines are intersected by a transversal, the corresponding angles have the same measure.

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Example Question #2 : How To Find An Angle Of A Line

Lines A and B in the diagram below are parallel. The triangle at the bottom of the figure is an isosceles triangle.

Act2

What is the degree measure of angle ?

Possible Answers:

Correct answer:

Explanation:

Since A and B are parallel, and the triangle is isosceles, we can use the supplementary rule for the two angles, and 2x+30 which will sum up to 180 . Setting up an algebraic equation for this, we get 4x+2x+30=180 . Solving for , we get x=25 . With this, we can get either 2(25)+30=80 (for the smaller angle) or 4(25)=100 (for the larger angle - must then use supplementary rule again for inner smaller angle). Either way, we find that the inner angles at the top are 80 degrees each. Since the sum of the angles within a triangle must equal 180, we can set up the equation as 80+80+y=180

y=20 degrees.

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HSPT Math : HSPT Mathematics

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #1404 : Concepts

Example Question #1402 : Concepts

Example Question #1403 : Concepts

Example Question #225 : Geometry

Example Question #771 : Ssat Upper Level Quantitative (Math)

Example Question #1 : How To Find An Angle In An Acute / Obtuse Triangle

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

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

Example Question #1 : How To Find An Angle Of A Line

Example Question #2 : How To Find An Angle Of A Line

All HSPT Math Resources

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