## Appendix B: Geometry

Using properties of angles to solve problems, learning outcomes.

- Find the supplement of an angle
- Find the complement of an angle

Are you familiar with the phrase ‘do a [latex]180[/latex]?’ It means to make a full turn so that you face the opposite direction. It comes from the fact that the measure of an angle that makes a straight line is [latex]180[/latex] degrees. See the image below.

[latex]\angle A[/latex] is the angle with vertex at [latex]\text{point }A[/latex].

We measure angles in degrees, and use the symbol [latex]^ \circ[/latex] to represent degrees. We use the abbreviation [latex]m[/latex] to for the measure of an angle. So if [latex]\angle A[/latex] is [latex]\text{27}^ \circ [/latex], we would write [latex]m\angle A=27[/latex].

If the sum of the measures of two angles is [latex]\text{180}^ \circ[/latex], then they are called supplementary angles. In the images below, each pair of angles is supplementary because their measures add to [latex]\text{180}^ \circ [/latex]. Each angle is the supplement of the other.

The sum of the measures of supplementary angles is [latex]\text{180}^ \circ [/latex].

The sum of the measures of complementary angles is [latex]\text{90}^ \circ[/latex].

## Supplementary and Complementary Angles

## Use a Problem Solving Strategy for Geometry Applications.

- Read the problem and make sure you understand all the words and ideas. Draw a figure and label it with the given information.
- Identify what you are looking for.
- Name what you are looking for and choose a variable to represent it.
- Translate into an equation by writing the appropriate formula or model for the situation. Substitute in the given information.
- Solve the equation using good algebra techniques.
- Check the answer in the problem and make sure it makes sense.
- Answer the question with a complete sentence.

An angle measures [latex]\text{40}^ \circ[/latex].

[latex]c=50[/latex] Step 6. Check:

[latex]50+40\stackrel{?}{=}90[/latex]

- Question ID 146497, 146496, 146495. Authored by : Lumen Learning. License : CC BY: Attribution
- Determine the Complement and Supplement of a Given Angle. Authored by : James Sousa (mathispower4u.com). Located at : https://youtu.be/ZQ_L3yJOfqM . License : CC BY: Attribution
- Prealgebra. Provided by : OpenStax. License : CC BY: Attribution . License Terms : Download for free at http://cnx.org/contents/[email protected]

To log in and use all the features of Khan Academy, please enable JavaScript in your browser.

## Unit 6: Lesson 4

- Find measure of vertical angles
- Find measure of angles word problem
- Equation practice with complementary angles
- Equation practice with supplementary angles
- Equation practice with vertical angles

## Unknown angle problems (with algebra)

- Your answer should be
- an integer, like 6 6 6 6
- an exact decimal, like 0.75 0.75 0 . 7 5 0, point, 75
- a simplified proper fraction, like 3 / 5 3/5 3 / 5 3, slash, 5
- a simplified improper fraction, like 7 / 4 7/4 7 / 4 7, slash, 4
- a mixed number, like 1 3 / 4 1\ 3/4 1 3 / 4 1, space, 3, slash, 4

- Arts & Music
- English Language Arts
- World Language
- Social Studies - History
- Holidays / Seasonal
- Independent Work Packet
- Easel by TPT
- Google Apps

## Interactive resources you can assign in your digital classroom from TPT.

## Easel Activities

## Easel Assessments

Unlock access to 4 million resources — at no cost to you — with a school-funded subscription..

## All Formats

Resource types, all resource types, results for problem solving with angles.

## Solve Problems With Angles - Modified/Differentiated

## Solving for Angles in Triangles Word Problems With Pictures

## Practice Worksheet: Problem Solving With Angles

## Angle Relationships (Vertical, Complementary, & Supplementary) | Puzzle

## Angles of Polygons | Coloring Activity

## Classifying Shapes and Angles CSI Math Murder Mystery with Geometry Wars

## Parallel Lines, Transversals, and Angles | Bingo Game

## Angle Relationships Task Cards | Parallel Lines, Transversals, & Angles Activity

Also included in: Angle Relationships Activity Bundle | Parallel Lines, Transversals, & Angles

## Parallel Lines, Transversals, and Angles | Cut and Paste Puzzle

## Project Based Learning Math Project Measuring Angles with Protractors

## Parallel Lines, Transversals, and Angles | Pyramid Sum Puzzle

## Measuring Angles with a Protractor Scavenger Hunt Activity

Also included in: Middle School Math Scavenger Hunt Mega Bundle - 45 Fun Low-Prep Math Activities

## Parallel Lines, Transversals, and Angles Puzzle - GOOGLE SLIDES VERSION!

Also included in: All Things Algebra® - Digital Activities Bundle for Google Slides™ - VOLUME 1

## Protractor Practice - Supplementary & Complementary Angles - Crack the Code

Also included in: Protractor Practice - Crack the Code Math Activities BUNDLED

## Unknown Angles Bingo Game PPT with Blank Bingo Card 7.G.B.5

## Angle Relationships Puzzle: DIGITAL VERSION (for Google Slides™)

## Angle Relationships With Algebra Foldable Notes - Using Equations

Also included in: Angle Relationships Activity Bundle - 5 Fun Low-Prep Activities - 7.G.B.5

## Angle Addition Postulate Task Cards

Also included in: Geometry Basics Activity Bundle

## Perpendicular and Angle Bisector Word Scramble

## 4th Grade Find Missing Angles Task Cards, Activities and DIGITAL LEARNING

Also included in: 4th Grade Angles and Measurement Bundle with Distance Learning

## COMPLEMENTARY, SUPPLEMENTARY, & VERTICAL ANGLES Scavenger Hunt Task Cards

## Relay Race Game BUNDLE (25 Games, 22 with 8 pages of 4 problems)

## ANGLES: ANGLE PAIRS - SCAVENGER HUNT WITH RIDDLE AND 20 TASK CARDS

## Trig Double Angle and Half Angle Identity Formulas Digital plus Print

Also included in: PreCalculus Unit 5 Analytic Trigonometry Digital Bundle Part 1 with Printables

TPT empowers educators to teach at their best.

## Keep in Touch!

## Angle Properties - Find the Angle Problems

In order to answer this type of questions,

- you would need to know some commonly used angle properties.
- you would need to practice lots of such problems. The more you practice, the easier it becomes to “see” which properties need to be applied.

## Some Common Angle Properties

The sum of angles at a point is 360˚.

The sum of complementary angles is 90˚.

The sum of angles on a straight line is 180˚.

Alternate Angles (Angles found in a Z -shaped figure)

Corresponding Angles (Angles found in a F -shaped figure)

The sum of angles in a triangle is 180˚.

An exterior angle of a triangle is equal to the sum of the two opposite interior angles.

The sum of interior angles of a quadrilateral is 360˚.

How to use the above angle properties to solve some “find the angle” problems?

Find the Measure of the Missing Angle

Angles and Parallel Lines : solving problems

Finding missing angles on two parallel lines, using corresponding angles and angles in a triangle.

Angles formed by Parallel Lines and Transversals

## Resources tagged with: Angles - points, lines and parallel lines

## Angles Inside

Draw some angles inside a rectangle. What do you notice? Can you prove it?

## Robotic Rotations

How did the the rotation robot make these patterns?

## Polygon Pictures

Can you work out how these polygon pictures were drawn, and use that to figure out their angles?

## Triangle in a Trapezium

## Isosceles Seven

Is it possible to find the angles in this rather special isosceles triangle?

## Polygon Rings

Join pentagons together edge to edge. Will they form a ring?

## Same Length

## Olympic Turns

## Which Solids Can We Make?

## Making Sixty

Why does this fold create an angle of sixty degrees?

## Age 5 to 7 Challenge Level

## Six Places to Visit

## How Safe Are You?

How much do you have to turn these dials by in order to unlock the safes?

## Round and Round and Round

## Semi-regular Tessellations

## Right Angles

Can you make a right-angled triangle on this peg-board by joining up three points round the edge?

## Subtended Angles

## Triangles in Circles

Can you find triangles on a 9-point circle? Can you work out their angles?

## Octa-flower

## Estimating Angles

How good are you at estimating angles?

## Watch the Clock

## Angle Trisection

## Quad in Quad

Join the midpoints of a quadrilateral to get a new quadrilateral. What is special about it?

## Flexi Quads

## Orbiting Billiard Balls

## Three Tears

Construct this design using only compasses

## Dotty Relationship

Can you draw perpendicular lines without using a protractor? Investigate how this is possible.

## Virtual Geoboard

## Pegboard Quads

## Angle Measurement: an Opportunity for Equity

Suggestions for worthwhile mathematical activity on the subject of angle measurement for all pupils.

## Watch Those Wheels

## Sweeping Hands

## Right Angle Challenge

How many right angles can you make using two sticks?

## Age 7 to 14

## Coordinates and Descartes

## Maurits Cornelius Escher

## Lunar Angles

## LOGO Challenge 7 - More Stars and Squares

## LOGO Challenge 8 - Rhombi

Explore patterns based on a rhombus. How can you enlarge the pattern - or explode it?

## LOGO Challenge 1 - Star Square

Can you use LOGO to create this star pattern made from squares. Only basic LOGO knowledge needed.

## Take the Right Angle

## Parallel Universe

## Similarly So

## A Problem of Time

## Square World

P is a point inside a square ABCD such that PA= 1, PB = 2 and PC = 3. How big is angle APB ?

## Clock Hands

## Account required

Already have a Studyladder account? Log In

New to Studyladder? Get a free trial account! Join Now

## Angles Problem Solving

- Course Mathematics
- Section Printable Worksheets
- Outcome Angles
- Activity Type Printable
- Activity ID 26702

## Activity: View similar activities

## Testimonials

What a brilliant site you have!!! I love it, especially as it saves me hours and hours of hard work. Others who haven't found your site yet don't know what they are missing! Patricia Celikbilek, Teacher Read More

It is quite frankly the best money I have ever spent on my child. I really cannot thank you enough for providing this, it really is brilliant. Vanessa Wills, Parent Read More

You have the most amazing program. Everybody loves it and the student's results have been in the high 90%'s, it's definitely due to your program. Chris Rayment, School Principal Read More

## Awarded June 2012 “Best Educational Website for Teaching and Learning”

Parent/teacher only, login required.

This activity requires an account to enable as it customises it questions to individual students

## Free Parent & Teacher Access

You can join Studyladder FREE!

I would like to register for a:

- Browse All / Search
- Mathematics
- Visual Arts and Music
- Health, Safety & Citizenship
- Language & Culture
- Information Communication Technology
- Theme Based Learning
- Forgot password

## Studyladder World Teaser

Studyladder home tutor trailer.

## IMAGES

## VIDEO

## COMMENTS

The six steps of problem solving involve problem definition, problem analysis, developing possible solutions, selecting a solution, implementing the solution and evaluating the outcome. Problem solving models are used to address issues that...

When multiplying or dividing different bases with the same exponent, combine the bases, and keep the exponent the same. For example, X raised to the third power times Y raised to the third power becomes the product of X times Y raised to th...

Opposite angles, known as vertically opposite angles, are angles that are opposite to each other when two lines intersect. Vertically opposite angles are congruent, meaning they are equal in degrees of measurement.

Solution: Step 1. Read the problem.

Use the math you already know to solve the problem. a. What is the measure of ZFOD? How do you know? b. Name two adjacent angles that together form ZFOD. What

Unknown angle problems (with algebra). CCSS.Math: 7.G.B.5. Problem. Solve for x x xx in the diagram below. Created with Raphaël x ∘ x^\circ x∘ ( 3 x + 10 )

In this lesson you will be given two angles, including one unknown. After being given the total combined angle you will need to determine

This is a pretty tricky problem. Can you solve for the angle? Watch the video for the solution. I thank Barry, and I thank Akshay Dhivare

How to calculate angles in polygons using the interior and exterior angle properties from http://mr-mathematics.com.

Art of Problem Solving's Richard Rusczyk discusses the relationships among angles formed when a transversal intersects parallel lines.

Solving for Angles in Triangles Word Problems With Pictures. 5 work sheets and 5 detailed answer keys. 10 pages total. Rules of parallel

Angles and Parallel Lines : solving problems. Finding missing angles on two parallel lines, using corresponding angles and angles in a triangle.

Resources tagged with: Angles - points, lines and parallel lines. Filter by: Content type: ALL, Problems, Articles, Games. Age range: All

Angles Problem Solving. Grade: All grades. Activity type: Printable. Printable resource - click here to open. ×. To save results or sets tasks for your