What students learn
Each floor of Vertex Tower teaches one angle relationship, starting with the simplest:
- Floor 1, The Gallery: complementary angles add to 90°.
- Floor 2, Server Room: supplementary angles add to 180°.
- Floor 3, Laser Lab: vertical angles, across from each other where two lines cross, are equal.
- Floor 4, Rail Yard: parallel lines cut by a transversal. Corresponding angles and alternate interior angles are equal.
- Floor 5, Penthouse Vault: co-interior (same-side interior) angles add to 180°. The last room, where the Golden Angle of Angels is kept, mixes all six relationships.
- Floor 6, The Algebra Vault (opens after Floor 5): one room of small equations with every relationship.
Every puzzle names its relationship and states its rule, so students connect the vocabulary to the picture each time. In the Algebra Vault the unknown angle is written as an expression, like x + 3: one angle is given, students find the other angle, then undo the + 3. That's the "write and solve a simple equation" part of 7.G.B.5, kept small enough to do in your head. Practice mode includes these too.
How the game works
Every room has two parts.
- The laser puzzle. A hologram shows the diagram with one given angle and one unknown, x. Students type x and fire. The laser turns by exactly the angle they typed, so a right answer hits the security panel and a wrong answer visibly misses, with the correct line shown next to it. Each room has three panels: the cameras, the guards' radios (slower, shorter-sighted guards) and the blueprints (shortcut doors open, the guards' routes are drawn and the lights stay on).
- The sneak. A top-down room with patrolling guards and sweeping cameras. Students move with the arrow keys (or an on-screen joystick), stay out of the light cones and the guards' red rings, hide behind cover, grab the diamond and reach the exit. Being seen fills an alert meter, faster the closer they are; stepping inside a red ring, or through a lit tripwire, alerts the guards at once.
Missed answers make the sneak harder. A missed camera panel adds a camera and makes the cameras faster and farther-seeing; missed radios make the guards faster and sharper-eyed with bigger red rings; missed blueprints turn the lights out except for a glow around the agent. Each miss also adds a blinking laser tripwire and another guard, and the 30-second timer becomes real: when it runs out, an alarm sends every guard after the agent. With zero right answers the sneak stays locked: students must redo all three panels, with new angles, until they hit at least one.
A way back. Students can redo the missed questions at any time (a button, or the R key) to switch that security off. After a missed panel, getting caught three times sends them back to the questions automatically. Each room awards up to three stars, one for each panel answered right on the first try, so stars measure the math, not the sneaking. Three right answers in a row earn a smoke bomb and five earn a decoy.
A wrong answer always shows how to solve it: a bar split into the two angles (for angles that add up) or two matching bars (for equal angles), then the steps one at a time.
- Story: five floors of three rooms, plus the Algebra Vault. A floor opens when the last room below it is cleared, and the bonus Algebra Vault opens after Floor 5.
- Practice: just the laser puzzles for any mix of the six relationships, with no guards and no timer.
Built-in thinking steps. On vertical and parallel-line puzzles, students first answer a quick check: are the angles equal, or do they add to 180°? After a hit, every angle in the diagram is labeled so students see the whole pattern. Wrong answers name the likely mistake (using 90 instead of 180, adding when they should subtract, undoing the + 3 the wrong way, a small subtraction slip). Which security system each panel controls changes every time, and rooms vary in size and layout and can appear mirrored, so a replay is never the same. Finishing Floor 5 plays a short ending as the agent escapes with the Golden Angle of Angels.
The printable worksheet's Part E uses game-style diagrams with the same "equal or add to 180°?" check.
Worked examples
Complementary: one angle is 34°. Find x.
34° + x = 90° x = 90° − 34° = 56°
Supplementary: two angles on a straight line; one is 118°.
118° + x = 180° x = 180° − 118° = 62°
Vertical: two lines cross; the marked angle is 49°. x is across from it.
Vertical angles are equal: x = 49°
Parallel lines: a transversal makes a 65° angle at the top crossing.
Corresponding or alternate interior angle: 65° (equal) Co-interior angle: 180° − 65° = 115°
Algebra Vault: one angle is 50° and its complement is x + 3.
50° + (x + 3) = 90° x + 3 = 40° x = 37°
Common mistakes
Using 180 for a complementary pair (or 90 for a supplementary one). Have students look for the right-angle box: if it's there, the pair adds to 90. The game names this mistake when it happens.
Assuming vertical angles add to 180°. Vertical angles are equal; it's the adjacent angles next to them that add to 180°.
Mixing up co-interior and alternate angles. Alternate angles are on opposite sides of the transversal and are equal; co-interior angles are on the same side and add to 180°.
Stopping at the whole angle in the Algebra Vault. If the angle is x + 3 and it measures 40°, the answer is x = 37, not 40. The game points this out: "That's the whole angle. Now find x."
Key vocabulary
Words and phrases to use when you talk through the game with students. Each one appears in the game, its questions or its feedback.
- complementary angles: two angles whose measures add to 90°
- supplementary angles: two angles whose measures add to 180°
- vertical angles: the angles across from each other where two lines cross; they are equal
- parallel lines: lines in the same plane that never meet
- transversal: a line that crosses two or more other lines
- corresponding angles: angles in the same position at each crossing; equal when the lines are parallel
- alternate interior angles: angles between the parallel lines, on opposite sides of the transversal; equal
- co-interior (same-side interior) angles: angles between the parallel lines, on the same side of the transversal; they add to 180°
Ways to use it in class
- Printables. A free worksheet with an answer key and a two-to-a-page exit ticket match this game, ready to print or save as a PDF.
- One floor per day. Teach a relationship, then play that floor. Progress is saved on each device, so students pick up where they left off.
- Targeted practice. Students who miss vertical angles on a quiz play Practice with only that relationship.
- Sketch the room. Students draw one puzzle diagram and label every angle they can find, not just the one asked.
- Exit ticket. "Two parallel lines are cut by a transversal. One angle is 72°. Label all eight angles."
Discussion questions
- Why do you only need to know one angle to find all eight when a transversal crosses two parallel lines?
- Can two complementary angles both be obtuse? Explain.
- If your answer were 10° too big, where would the laser go? How would you know from the picture before firing?
Real-world connections
Camera and floodlight coverage, road intersections, railroad crossings, and the crossing beams of bridges and ladders all depend on these relationships. Carpenters use supplementary angles every time they cut two boards to meet in a straight line.
Standards
CCSS.MATH.CONTENT.7.G.B.5Use 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.
CCSS.MATH.CONTENT.8.G.A.5Use informal arguments to establish facts about the angles created when parallel lines are cut by a transversal. (Floors 4 and 5)
Access and privacy
No accounts, no data collected. Stars, diamonds and unlocked suits are saved only in the student's own browser and are never sent anywhere. Plays with the keyboard alone, or with an on-screen joystick and number pad on a tablet, and works with screen readers.