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Fraction Classroom · 2.3.0 · Student pages

Measure an angle by its turn, not its ray length

Use a shared vertex and a circular turn to explain degree measure, then compare angles even when their drawn rays have different lengths.

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The labelled turns are 60°, 90° and 120°. Ray endpoints only limit the drawing; the turn at the shared vertex determines angle size.60°90°120°
The labelled turns are 60°, 90° and 120°. Ray endpoints only limit the drawing; the turn at the shared vertex determines angle size.

Build the idea

model. Two angles both turn through 60 one-degree steps. One drawing has much longer rays. Which angle has the greater degree measure?

  1. Find the common endpoint, called the vertex, and follow the direction of each ray from it. The opening between those directions defines the angle.
  2. Imagine rotating one ray around the vertex until it reaches the other ray. A full turn contains 360 equal one-degree steps.
  3. Count the steps in the opening: sixty one-degree turns make a 60-degree angle. Compare it with a 90-degree quarter turn and a 120-degree angle.
  4. Extend either ray without rotating it. The directions are unchanged, so the same sixty steps still connect them. Do not use ray length as the angle measure.

Worked example: Neither. Both measure 60 degrees. Extending a ray changes the drawing's length, not the turn between the directions.

Practise and explain

Try p1–p3 with a partner. Use a drawing and label your units. Try e1 independently before comparing responses.

p1. An angle turns through 75 one-degree steps. What is its measure in degrees?

p2. A 40-degree angle has both rays extended without rotation. What is its new measure in degrees?

p3. A full turn is 360 degrees. How many degrees are in one quarter of a full turn?

e1. An angle contains 110 one-degree turns. Its rays are shortened in the drawing but keep their directions. State the angle measure and explain why.

Transfer the idea

transfer. An angle drawing is turned upside down without changing its shape. Does its degree measure change? Explain how you could check.