We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

HSPT Math : Geometry

Study concepts, example questions & explanations for HSPT Math

Create An Account

All HSPT Math Resources

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

Example Questions

← Previous 1 2 … 23 24 25 26 27 28 29 30 31 … 34 35 Next →

Example Question #6 : How To Find An Angle

Thingy

Note: Figure NOT drawn to scale.

In the above figure, $m \angle 1=\left ( x+17 \right )^{\circ}$ and $m \angle 2= \left (7x+11 \right )^{\circ}$ . Which of the following is equal to $m \angle 1$ ?

Possible Answers:

$36^{\circ}$

$26^{\circ}$

$7\frac{3}{4}^{\circ }$

$21\frac{5}{7}^{\circ}$

$29\frac{5}{7}^{\circ}$

Correct answer:

$36^{\circ}$

Explanation:

$\angle 1$ and $\angle 2$ form a linear pair, so their angle measures total $180^{\circ}$ . Set up and solve the following equation:

$m \angle 1+ m \angle 2 = 180^{\circ}$

$\left ( x+17 \right ) + \left (7x+11 \right ) = 180$

8x+28 = 180

8x=152

x = 19

$m \angle 1=\left ( x+17 \right )^{\circ} = \left ( 19+17 \right )^{\circ} = 36^{\circ}$

Report an Error

Example Question #261 : Geometry

Two angles which form a linear pair have measures $(2x+72)^{\circ}$ and $(5x-125)^{\circ}$ . Which is the lesser of the measures (or the common measure) of the two angles?

Possible Answers:

$81\frac{1}{2} ^{\circ }$

$22\frac{6}{7}^{\circ}$

$33\frac{2}{7}^{\circ }$

$65\frac{2}{3 } ^{\circ }$

$41\frac{3}{7}^{\circ}$

Correct answer:

$41\frac{3}{7}^{\circ}$

Explanation:

Two angles that form a linear pair are supplementary - that is, they have measures that total $180^{\circ}$ . Therefore, we set and solve for in this equation:

(2x+72)+(5x-125)= 180

7x - 53 = 180

7x = 233

$x = \frac{233}{7}= 33 \frac{2}{7}$

The two angles have measure

$2 \cdot 33 \frac{2}{7} +72= 138 \frac{4}{7} ^{\circ}$

and

$5 \cdot 33 \frac{2}{7} -125 = 41\frac{3}{7}^{\circ}$

$41\frac{3}{7}^{\circ}$ is the lesser of the two measures and is the correct choice.

Report an Error

Example Question #261 : Geometry

Two vertical angles have measures $(3x+14)^{\circ }$ and $\left ( 5x-17\right )^{\circ }$ . Which is the lesser of the measures (or the common measure) of the two angles?

Possible Answers:

$15\frac{1}{2}^{\circ }$

$22\frac{7}{8}^{\circ}$

$60\frac{1}{2} ^{\circ }$

$68\frac{5}{8}^{\circ}$

$41\frac{1}{8}^{\circ}$

Correct answer:

$60\frac{1}{2} ^{\circ }$

Explanation:

Two vertical angles - angles which share a vertex and whose union is a pair of lines - have the same measure. Therefore, we set up and solve the equation

3x+14= 5x-17

14= 2x-17

2x= 31

$x= 15\frac{1}{2}$

$3x+14 = 3 \cdot 15\frac{1}{2} + 14 = 46\frac{1}{2} + 14= 60\frac{1}{2} ^{\circ }$

Report an Error

Example Question #9 : How To Find An Angle

A line intersects parallel lines and . $\angle 1$ and $\angle 2$ are corresponding angles; $\angle 1$ and $\angle 3$ are same side interior angles.

$m \angle 1 = \left (3x+2y \right )^{\circ }$

$m \angle 2 = \left ( 4x+21\right )^{\circ }$

$m \angle 3 = \left ( 2y-27\right )^{\circ}$

Evaluate x+y .

Possible Answers:

x+y = 120

x+y = 60

x+y = 30

x+y = 45

x+y = 90

Correct answer:

x+y = 60

Explanation:

When a transversal such as crosses two parallel lines, two corresponding angles - angles in the same relative position to their respective lines - are congruent. Therefore,

3x+2y = 4x+21

3x+2y- 3x - 21 = 4x+21 - 3x - 21

x = 2y - 21

Two same-side interior angles are supplementary - that is, their angle measures total 180 - so

3x+2y + 2y-27 = 180

3x+4y-27 = 180

3x+4y= 207

We can solve this system by the substitution method as follows:

3( 2y - 21)+4y= 207

6y-63+4y= 207

10y-63= 207

10y = 270

y = 27

Backsolve:

x = 2y - 21

x = 2 (27)- 21 = 54-21 = 33

x+y = 27+33 = 60 , which is the correct response.

Report an Error

Example Question #1 : How To Find An Angle

Vertical_angles

Note: Figure NOT drawn to scale.

Refer to the above diagram. Give the measure of $\angle 1$ .

Possible Answers:

$88^{\circ }$

$128^{\circ }$

$144^{\circ }$

$96^{\circ }$

$120 ^{\circ }$

Correct answer:

$120 ^{\circ }$

Explanation:

The top and bottom angles, being vertical angles - angles which share a vertex and whose union is a pair of lines - have the same measure, so

2x+y = 2y ,

or, simplified,

2x+y - y= 2y - y

y = 2x

The right and bottom angles form a linear pair, so their degree measures total 180. That is,

2y+ 8x = 180

Substitute for :

2(2x)+ 8x = 180

4x+8x = 180

12x= 180

x = 15

The left and right angles, being vertical angles, have the same measure, so, since the right angle measures $\left (8x \right )^{\circ } =\left (8 \cdot 15 \right )^{\circ } = 120 ^{\circ }$ , this is also the measure of the left angle, $\angle 1$ .

Report an Error

Example Question #1 : Coordinate Geometry

Math4

What is the measurement of $\angle B$ ?

Possible Answers:

120

Correct answer:

Explanation:

If you extend the lines of the parellelogram, you will notice that a parellogram is the same as 2 different sets of parellel lines intersecting one another. When that happens, the following angles are congruent to one another:

Math4-p1

Therefore, x = 60

Report an Error

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

Report an Error

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:

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

Report an Error

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.

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

Report an Error

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.

Report an Error

← Previous 1 2 … 23 24 25 26 27 28 29 30 31 … 34 35 Next →

View Tutors

Reuben
Certified Tutor

University of Alberta, Bachelor of Science, Mathematics.

View Tutors

Aaron
Certified Tutor

Portland State University, Bachelors, Economics. Portland State University, Masters, Environmental and Resource Management.

View Tutors

Chase
Certified Tutor

Western Governors University, Bachelor of Science, Mathematics.

All HSPT Math Resources

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

Popular Subjects

ISEE Tutors in San Diego, ISEE Tutors in Miami, Statistics Tutors in Philadelphia, GRE Tutors in Dallas Fort Worth, Computer Science Tutors in Miami, English Tutors in Houston, Reading Tutors in San Diego, ACT Tutors in Dallas Fort Worth, Reading Tutors in Chicago, Physics Tutors in Atlanta

Popular Courses & Classes

GRE Courses & Classes in Los Angeles, GRE Courses & Classes in Dallas Fort Worth, SSAT Courses & Classes in Philadelphia, Spanish Courses & Classes in Miami, SAT Courses & Classes in Denver, ACT Courses & Classes in Phoenix, GRE Courses & Classes in Atlanta, ISEE Courses & Classes in Boston, ISEE Courses & Classes in Chicago, Spanish Courses & Classes in San Diego

Popular Test Prep

SAT Test Prep in San Diego, GMAT Test Prep in Phoenix, SSAT Test Prep in Boston, MCAT Test Prep in Seattle, ISEE Test Prep in Phoenix, MCAT Test Prep in Boston, GRE Test Prep in Phoenix, ISEE Test Prep in Dallas Fort Worth, LSAT Test Prep in New York City, SAT Test Prep in Boston

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

HSPT Math : Geometry

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #6 : How To Find An Angle

Example Question #261 : Geometry

Example Question #261 : Geometry

Example Question #9 : How To Find An Angle

Example Question #1 : How To Find An Angle

Example Question #1 : Coordinate Geometry

Example Question #261 : Geometry

Example Question #262 : Geometry

Example Question #261 : Geometry

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

All HSPT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: