7th Grade Angle Relationships and Equations Lesson (Free PDF)
This grade 7 angle relationships lesson for 7th Grade covers angle relationships and equations (Common Core 7.G.B.5), with a free PDF to print.
Two angles are complementary if their measures add up to 90 degrees and supplementary if they add up to 180 degrees. Angles on a straight line are supplementary, and vertical angles, which are opposite each other where two lines cross, are equal. You can write and solve a simple equation to find an unknown angle.
Grade 7 · Common Core State Standards: 7.G.B.5
Key facts in this grade 7 angle relationships lesson
- Complementary angles add to \(90^{\circ}\); supplementary angles add to \(180^{\circ}\).
- Angles on a straight line add to \(180^{\circ}\); angles around a point add to \(360^{\circ}\).
- Vertical angles are equal.
- Adjacent angles share a vertex and a side.
- Write an equation from the relationship, solve it, and check the sum.
What are complementary and supplementary angles?
Two angles are complementary if their measures add up to \(90^{\circ}\). Two angles are supplementary if their measures add up to \(180^{\circ}\).
If one angle is \(35^{\circ}\), its complement is \(90 – 35 = 55^{\circ}\). If one angle is \(112^{\circ}\), its supplement is \(180 – 112 = 68^{\circ}\). A straight line makes \(180^{\circ}\), and two angles that share a side and form a straight line are a linear pair.
What are vertical angles?
When two lines cross, they make four angles. Angles that are across from each other are vertical angles, and vertical angles are always equal.
How do you write an equation for an unknown angle?
- Decide the relationship: sum of 90, sum of 180, equal, or sum of 360 around a point.
- Write an equation using the angle expressions.
- Solve it with inverse operations.
- Substitute to find each angle and check the sum.
Example. Two supplementary angles measure \((3x + 10)^{\circ}\) and \((x + 30)^{\circ}\). Then \(3x + 10 + x + 30 = 180\), so \(4x + 40 = 180\), which gives \(x = 35\). The angles are \(115^{\circ}\) and \(65^{\circ}\), and \(115 + 65 = 180\).
Angles around a single point add up to \(360^{\circ}\). Three angles on a straight line add up to \(180^{\circ}\). Use these facts to find unknown angles in any diagram, and always check that your answers make sense: an angle in a picture that looks acute cannot be \(120^{\circ}\).
Grade 7 angle relationships lesson: questions and answers
What is the difference between complementary and supplementary angles?
Complementary angles add up to \(90^{\circ}\) and supplementary angles add up to \(180^{\circ}\). A way to remember: C comes before S, and 90 comes before 180.
What are vertical angles?
Vertical angles are the angles opposite each other when two lines cross. They have the same measure.
How do you find the supplement of an angle?
Subtract the angle from 180. The supplement of \(112^{\circ}\) is \(180 – 112 = 68^{\circ}\).
Are adjacent angles always supplementary?
No. Adjacent angles are supplementary only when together they form a straight line. Adjacent angles in a right angle are complementary.
How do I solve for x in an angle problem?
Write an equation that matches the relationship, such as \(x + 65 = 90\), and solve it with inverse operations. Then check that the angles add up correctly.
How to use this grade 7 angle relationships lesson
Read the definitions first, then follow the worked method line by line and redo the example on paper without looking. When every step makes sense, move on to the worksheet, then check yourself with the quiz.
Download the grade 7 angle relationships lesson as a PDF with the button below and keep it with your notes.
All Grade 7 chapters: Grade 7 math.
More 7th Grade math
Lessons
See all
Worksheets
See all
Tests
See all
Solving Real-World Problems with Rational Numbers Test with Point Values- Probability and Probability Models Test with Point Values
- Area, Volume and Surface Area Test with Point Values
- Equivalent Linear Expressions Test with Point Values
- Random Sampling and Inference Test with Point Values
- Multiplying and Dividing Rational Numbers Test with Point Values
