Grade 10 — Mathematics 10-3 › T3U08 Lines & Angles

Grade 10 › T3U08 Lines & Angles › L2
GRADE 10 · ALBERTAOUTCOME AB-MAT10-3-G6

L2 · Drawing, replicating and constructing angles (including reflex)

Learning goal

“I can draw, estimate, measure, replicate and bisect angles of all five types - acute, right, obtuse, straight and reflex - using referent angles to estimate, a protractor to measure, and compass-and-straightedge (or a Mira or carpenter's square) to copy an angle exactly. For a reflex angle I know the protractor only reads the smaller side, so I measure that and subtract from 360°.”

Reflex angle — an angle greater than 180° and less than 360°: the "long way around" between two arms.
Referent angle — a known angle size (22.5°, 30°, 45°, 60°, 90°, 180°) you compare an unknown angle against to estimate it.
Replicate — to copy an angle exactly onto a new location, so the copy measures the same as the original.
Bisect — to split an angle into two equal angles (the bisector ray is located by equal compass arcs).
Worked example

The five types, by measure: acute (less than 90°), right (exactly 90°), obtuse (between 90° and 180°), straight (exactly 180°), reflex (between 180° and 360°). Estimate first, with referents: an angle that opens a bit wider than the 45° referent but clearly less than 90° is "about 60°" - the 60° referent confirms it. Now measure a reflex angle. Two arms make a smaller angle of 130° on one side and the reflex angle on the other. A protractor can only read up to 180°, so it reads the smaller side: 130°. The reflex angle is the rest of the full turn: 360° - 130° = 230°. Say it plainly: a full turn is 360°. Whatever the protractor reads, the reflex angle on the other side is 360° minus that reading - never the reading itself.

Check yourself — explain it

A protractor alone can't give a reflex angle's measure directly because...

Paired problem — example still visible

The smaller angle between two arms is 85°. Find the reflex angle on the other side. -> 275° (360 - 85)

Faded completion — last step is yours

"To measure a reflex angle: read the smaller angle with the protractor, then subtract it from ___." -> 360°

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10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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