Lines and Angles
Lessons in this chapter
About Lines and Angles
Lines and Angles teaches kids to reason about angle measures algebraically instead of just measuring them, using a handful of angle relationships that show up constantly in geometry from here on.
Identify different angle relationships introduces complementary angles (summing to 90°), supplementary angles (summing to 180°), vertical angles (formed by two intersecting lines, always equal), and adjacent angles (sharing a vertex and a side): the vocabulary every angle problem in the rest of the chapter relies on.
Find unknown angle measures uses those relationships to set up and solve for a missing angle: if two angles are supplementary and one is 65°, the other must be 115°, found by subtracting from 180° rather than measuring.
Apply the angle sum property and exterior angles property for triangles closes the chapter with two triangle-specific rules: the three interior angles of any triangle always sum to 180°, and an exterior angle of a triangle always equals the sum of the two non-adjacent interior angles, both of which turn a triangle with two known angles into one with every angle solvable.
Each of the three lessons is a 7th grade math worksheet worked in the page: Identify Different Angle Relationships, Find Unknown Angle Measures and Apply the Angle Sum Property and Exterior Angles Property for Triangles are practice questions on real diagrams rather than a reference sheet of angle facts. The marking is per question, so a wrongly named angle pair is corrected before it is used in the next calculation. All three are free to try, with no login needed for your first 3.
Frequently asked questions
Identify Different Angle Relationships comes first, naming complementary, supplementary, vertical and adjacent angles. Find Unknown Angle Measures then uses those relationships to set up and solve for a missing angle, often as an equation. Apply the Angle Sum Property and Exterior Angles Property for Triangles closes the chapter with the 180 degree rule and the exterior angle result. This sits in the Common Core domain Geometry (7.G).
Complementary angles add up to exactly 90° (like 30° and 60°); supplementary angles add up to exactly 180° (like 110° and 70°). The easiest way to remember which is which: ‘c’ for complementary comes before ‘s’ for supplementary in the alphabet, and 90 comes before 180.
Vertical angles are the pair of opposite angles formed when two lines cross. They’re always equal because they’re both formed the same way, by the same two lines, just facing opposite directions. Identify Different Angle Relationships has kids spot this pattern in a diagram before using it to solve for a missing angle.
Adjacent angles share a vertex (corner point) and a side, sitting right next to each other without overlapping: unlike vertical angles, which sit across from each other. Two adjacent angles that together form a straight line are also supplementary.
Subtract the known angle from the total: if two angles are complementary and one is 35°, subtract 35° from 90° to get 55°; if they’re supplementary and one is 65°, subtract 65° from 180° to get 115°. Find Unknown Angle Measures is entirely built on this one subtraction move, applied to different starting totals.
The three interior angles inside any triangle always add up to exactly 180°, no matter the triangle’s shape or size, so if two angles are known, the third is found by subtracting their sum from 180°.