Compare five angle drawings, then change their rotation and displayed ray length to see which properties stay the same. G1 and G2 both have 50° openings, even though G2 begins at 70° and ends at 120°. Students enter a degree measure and category; the fixed check compares the declared angle while a teacher reviews the measurement explanation.
Identify the vertex and two rays
An angle is formed by rays sharing a vertex. The OpenStax angle section describes this model, degree classifications, and centering a protractor at the vertex. Use those relationships to compare the five drawings.
Use positive openings no greater than 180° in this bounded activity. G1 has a 50° smaller opening. G2 has the same 50° opening but rotates both rays together and shortens their visible segments. Mathematical rays extend indefinitely; only the portions drawn on the page become shorter.
For a concrete drawing specification, G1's first ray points right and its second ray turns 50° counterclockwise from it. In G2, rotate both directions 70° counterclockwise: they now point at 70° and 120° from the original rightward direction. The difference is still 120 - 70 = 50°. The smaller opening has not increased to 120°.
Follow the arc around the shared vertex to identify the opening being measured. The page lists the starting and second ray directions, so you can compare their difference after a rotation.
Keep the complete five-figure key
| Figure | Declared opening | Category | What the comparison checks |
|---|---|---|---|
| G1 | 50° | Acute | Initial opening |
| G2 | 50° | Acute | Whole-figure rotation and shorter displayed segments |
| G3 | 90° | Right | Exact right-angle boundary |
| G4 | 130° | Obtuse | Between right and straight |
| G5 | 180° | Straight | Opposite rays at the straight-angle boundary |
Within this positive-opening scope, acute means less than 90°, right is exactly 90°, obtuse is greater than 90° and less than 180°, and straight is exactly 180°. A vertical-looking ray does not by itself make the opening right, and a slanted figure does not by itself make it acute.
Enter the degree measure and category in the blank fields before using Reveal to view the current key. The explanation prompt can ask, “What changed between G1 and G2? What evidence shows the angle stayed the same?”
Start the protractor scale at the chosen ray
For G1, align the protractor's center with the shared vertex. Align its zero baseline with the first, rightward ray. Follow the scale that begins at zero on that starting side, then read where the second ray crosses it.
The intended opening is 50°, not 130° from the opposite scale. A dual-scale protractor can show both numbers at the same mark; reading the larger number without identifying the baseline measures the supplementary opening instead.
For G2, align the protractor with G2's rotated first ray. Do not leave the protractor's baseline on the page's horizontal axis and call the second ray's page direction the angle. The instrument must move with the chosen baseline and keep its center at the vertex.
Work through the measurement in order: locate the vertex, center the protractor, identify the starting ray's zero, and read the second ray. Then write why that reading supports your category. The page checks the supplied numeric measure and category; a teacher reviews how you measured.
Transform the display
Choose a figure, then change Rotation or Display length. Apply display redraws both directions together and clears old answers and feedback. The selected opening remains fixed. Length is the drawn segment length, not the extent of a mathematical ray. The local controls accept rotation 0–360° and length 40–110 logical pixels.
G3 is exactly 90° and right; G4 is 130° and obtuse; G5 is 180° and straight. The answer check uses these supplied mathematical values, not a claim that a learner physically measured the screen. Align the protractor to the rotated first ray before reading the second. Reveal shows the current key separately, and Clear answers leaves the displayed figure in place.
Copy a prompt for this example
Build a single self-contained HTML angle activity with embedded CSS, JavaScript, and original SVG drawings. Use a geometry-notebook layout with a large drawing, figure buttons, display controls, and clearly separated answer and explanation fields. Keep text readable and the layout comfortable on a narrow screen.
Provide G1 with a 50° opening, starting direction 0°, and displayed length 90. G2 has the same 50° opening, starting direction 70°, and length 55. G3 is 90° and right, G4 is 130° and obtuse, and G5 is 180° and straight. G1 and G2 are acute. Show two rays sharing a marked vertex and an arc identifying the opening.
Allow rotation from 0 through 360 degrees and displayed length from 40 through 110 logical pixels. Apply display must transform both rays together, preserve the opening, and clear previous responses. Reject invalid display values and require a valid applied drawing before checking answers.
Ask for a positive degree measure up to 180, a category, and a written measurement explanation. Check the declared measure and category against the selected figure. Leave physical measurement and explanation review to the teacher.
Include a separate key reveal and Clear answers. Figure selection restores that figure's display settings. Explain that G2's directions of 70° and 120° differ by 50°, and that shorter drawn segments do not shorten mathematical rays. Return only the complete HTML file.
For a comparison at the board, NOS can display this prepared HTML ray activity. Rotate G2, shorten its segments, and ask students to explain 120 - 70 before revealing that its opening still matches G1.