Geometry and measurementGrade 7
Vertical angles worksheets
Each problem draws two crossing lines with one angle given. Students find the vertical or adjacent angle, or solve an equation for x. This page uses the shared angle generator, so you can also switch to other angle facts.
- Fresh problems every time
- Answer key on its own page
- Print or PDF, Letter or A4
- Free, no sign-up
On this page
Two lines, four angles
When two straight lines cross, they form four angles. The ones facing each other across the crossing point are called vertical angles, and they are always equal. The ones sitting side by side share a ray and make a straight line together, so they add to 180°. Those two facts are enough to find every angle in the picture from any one of them.
This sheet is aimed at seventh grade. Students should know what a degree is and be able to subtract from 180. Beyond it, the same two facts carry into geometry proofs and into missing angles in triangles.
Two ways to use the page
The Problems menu has the options that matter here:
- Vertical angles. The figure shows one angle in degrees and a letter x on another. In about six of ten problems x is the vertical partner, so x equals the given angle. In the rest x is a neighbor, and the student must subtract from 180°. Mixing the two forces students to look at the picture before choosing a rule.
- Vertical angles with equations. One angle is labeled with an expression such as (3x + 7)°, and its vertical partner shows a number of degrees. Students set the expression equal to the number and solve for x. The answer is a whole number from 4 to 20, and the key gives x itself, not the angle.
The same menu also offers angles on a straight line, angles around a point, complementary and supplementary pairs, triangle angles and a mixed set. Those are useful for review but they change what the sheet teaches, so pick one at a time. Eight problems is the default; use 4 for a first look and up to 16 for a unit review.
Worked example: (3x + 7)° across from 49°
- Name the relationship. The two angles face each other across the crossing, so they are vertical angles and equal.
- Write the equation. 3x + 7 = 49.
- Subtract 7 from both sides. 3x = 42.
- Divide by 3. x = 14.
- Check. 3 × 14 + 7 = 49. Yes.
A plain example: if the given angle is 65° and x sits next to it on the same line, then x = 180° − 65° = 115°. If x sits across from 65°, then x = 65°. The picture decides.
Mistakes the key will expose
- Treating neighbors as equal. A student who answers 65° for an adjacent angle has matched the numbers without reading the diagram. The key gives 115°.
- Subtracting from 90° instead of 180°. This mixes up complementary and supplementary angles.
- Answering with the angle instead of x. On the equation sheet the key shows x = 14, not 49°. Ask for both if you want a complete answer.
- Dropping the degree sign. In plain mode the key writes the angle with ° after it. A bare number can mean something different.
- Algebra slips. Subtracting 7 from only one side, or dividing only the 3x. A quick substitution check catches nearly all of them.
Building the habit
Before computing anything, have students mark the given angle with a colored pencil and shade its vertical partner in the same color. Then the two unmarked angles must be the other pair. For students who find the equation form tricky, start with one-step equations and return when 3x + 7 = 49 feels routine. Once confident, they can create their own problem by drawing crossing lines and giving a classmate a single angle.