Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.
Official wording from the Common Core State Standards for Mathematics (© 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers). View on thecorestandards.org
When two lines cross, they make four angles, and those angles are not independent: opposite (vertical) angles are equal, and neighbors along a line add to 180 degrees. Seventh graders put angle facts like these to work in multi-step problems, writing and solving equations to find unknown angles in a figure.
The key relationships are complementary angles, which add to 90°, supplementary angles, which add to 180°, vertical angles, which are equal, and adjacent angles, which share a vertex and a side so that their measures can be added together. A typical problem labels angles with expressions such as x and 2x + 15 and states that they form a straight line. Students recognize the relationship, write the equation x + 2x + 15 = 180, solve it, and then substitute back to find each angle. This standard is a natural meeting point of geometry with the equation-solving skills in 7.EE.B.4.
Students swap 90 and 180. A memory aid helps: complementary goes with a corner (right angle), supplementary goes with a straight line.
Finding x = 55 is not the same as finding the angle 2x + 15. Ask students to circle what the question asks for before they start.
Adjacent angles only add to 180° when their outer sides form a straight line. Two adjacent angles inside a right angle add to 90°, for example.
Vertical angles are the opposite angles at a vertex where two lines cross, whatever direction the lines run. The name comes from 'vertex'.
Two angles form a straight line. One measures x° and the other measures (2x + 15)°. Find both angles.
Answer: The angles measure 55° and 125°.
Use paper cutouts or a protractor on crossing straws to let students measure vertical angles and see they always match before stating the rule. Then move quickly to diagrams labeled with expressions, since the standard's emphasis is on writing and solving equations.
State tests often present a figure with three or four angles around a point or along a line and one or two expressions. Students who first name the relationship in words ('these two are vertical, so they are equal') set up the equation correctly far more often.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: 56 (also accepted: 56°, 56 degrees)
Complementary angles add to 90°: 90 - 34 = 56°.
Answer: 20 (also accepted: x = 20, x=20)
Vertical angles are equal, so 3x + 10 = 70. Then 3x = 60 and x = 20.
Answer: B) 36°
x + 4x = 180, so 5x = 180 and x = 36°. The larger angle is 144°.
Answer: C) Vertical angles
Vertical angles are opposite each other where two lines cross, and they are always equal. The other pairs only have a fixed sum or a shared side.
Answer: 50 (also accepted: x = 50, x=50)
30 + x + 2x = 180, so 3x = 150 and x = 50.
Answer: A) 50°
2x + x + 15 = 90, so 3x = 75 and x = 25. Angle A = 2 × 25 = 50°.
A full lesson with slides, activities and an exit ticket on supplementary, complementary and vertical angles, pitched to grade 7 and editable in PowerPoint or Google Slides.
Make a lesson →A printable, differentiated worksheet on 7.G.B.5 with an answer key, ready in about a minute.
Make a worksheet →Turn supplementary, complementary and vertical angles into a quiz students answer online that marks itself, with a class summary for you.
Build a test →Adjacent angles sit side by side, sharing a vertex and one side. Vertical angles are across from each other where two lines intersect and share only the vertex.
No. Angles formed when a transversal crosses parallel lines are part of eighth grade (8.G.A.5). Seventh grade focuses on complementary, supplementary, vertical and adjacent angles.