Unknown Angles Worksheets
Over the years we have learned so much about geometry that we have several definitively proven rules that we can use to our advantage to find the value of measures such as angles that we do not have the ability to measure with actual tools. This helps us in all walks of life from determining the length of a board on our back deck to physicists using these principles to determine the likely of a sub-atomic particle being located in a certain region in an atom of helium. These worksheets and lessons will help you learn how to identify the measures of angles that are unknown by using others as a reference.
Aligned Standard: Grade 7 Geometry - 7.G.B.5
- Finding Angles Step-by-step Lesson- My husband uses this trick all the time now. He's building a deck out back.
- Guided Lesson - Three great scenarios of finding missing angles of triangles.
- Guided Lesson Explanation - Once you understand the first one, all the others are a breeze.
- Practice Worksheet - The jungle is running wild with all types of missing angles. Find them all.
- Angles Five Worksheet Pack - Hope you brushed up on your angle vocabulary for this one.
- Matching Worksheet - Match the missing measures of angles to the shapes that are missing them.
- Each Interior Angle Worksheet Five Pack - How many sides do these shapes have and what are their angles?
- Answer Keys - These are for all the unlocked materials above.
Homework Sheets
We go absolutely triangle and line crazy with these.
- Homework 1 - Write and solve an equation to find the measure of angle x.
- Homework 2 - Find the measure of angle x.
- Homework 3 - All three angles are on the same line so the value of all the angles is 180°.
Practice Worksheets
Please help students notice that some of these angles are not drawn to scale on purpose.
- Practice 1 - What is the value of g? Given
- Practice 2 - Find the missing angle measurement in each set of complementary angles. Assume a right angle is formed.
- Practice 3 - The sum of all angles within a triangle = 180°
Math Skill Quizzes
Use the other angles as a reference and find all the missing angles.
- Quiz 1 - What is the value of p?
- Quiz 2 - Because these are vertical angles that are formed opposite each other when the two lines intersect. Vertical angles are congruent.
- Quiz 3 - Using Double Triangles to Solve Angle Measures
How to Identify the Measures of Unknown Angles
Geometry is a very powerful form of math. It can help us make ridiculously accurate calculations about things we cannot even see. The geometry behind angles is one of the more frequently used applications of this math in the real world. To simply put, an angle is the space between two straight lines that start at the same point. The straight lines are known as the segments, and the point where both lines meet is known as the vertex.
But do all angles look the same? Some angles combine together to give us a single figure of angle. Here are the different types of these angles you may come across:
Complementary - In some cases, two angles meet to form a single figure. Complementary angles are angles in which two angles meet to form a single angle. The sum of these angles is measured to be 90 degrees. You can create these measures in the real world by using a T-square.
Supplementary - Supplementary angles are another type of angle where two angles meet to form a single angle. But in this type of angle, the sum is measured to be 180 degrees. I you have a straight edge, you can replicate these values.
Vertical - Vertical angles are formed when two lines cross each other. The term vertical here doesn't mean an up or down direction; it means that they share the same corner point. The interesting thing about the vertical angle is that they measure the same.
Adjacent - When two angles share a common side and a common corner point, they are called an adjacent angle. These angles lie side by side but never overlap.
Triangles have some very helpful properties. Maybe that is why a whole branch of mathematics (trigonometry) is dedicated to them. Here are some very unique things about triangles that we can use to better understand all types of different measures:
- The sum of all three angles in a triangle is 180 degrees. This means that in a right triangle the other two angles must be equal to 90 degrees.
- The exterior angle of a triangle has the same measure as adding the interior opposite angles.
There are many more properties that we can explore, but for right now these are helpful enough to explore and find the measures of many different unknown angles.