Math · Stage 6

Chase angles and dissect areas in composite figures

A missing angle is never really missing — a straight line, a point, a triangle or a pair of parallel lines always pins it down. And an odd-looking shape is only a few neat rectangles and triangles in disguise, waiting to be added up (or taken back).

✦ Math📘 Stage 6 · S6⏱ ~14 min🧒 Ages 10–12★ Free to start

I can chase angles and dissect areas in composite figures.

Start the free lesson →⬇ Printable PDF

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Kavi and the Puzzle Garden 🧭

Kavi found a garden shaped like a wonky letter L 🌿 with one angle rubbed off the map. “How do I measure what I can't see?” 🤔 Then Kavi noticed the clues: three angles met around the fountain and had to add to 360°, so the missing one was forced to be exactly 90°. And the lawn? Kavi drew one line and the L split into two tidy rectangles — 2×6 + 5×2 = 22 m². “Nothing was missing,” grinned Kavi. “I just had to chase the angle and cut the shape into pieces.”

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What your child will learn

1Every arrangement has a target sumAngle-chasing works because each way angles can meet has a fixed total. Learn the four big ones, then sort each arrangement into the total it must add up to →

2Name the arrangement, read off the ruleYou rarely get the angle directly — you chase it through one or two of these rules. Tap each line to hear it.

3An L-shape is two rectangles in disguiseDraw one line and the L breaks into a tall rectangle A and a foot rectangle B that do not overlap. Tap each part to see its area.

4Add the pieces, or surround and subtractTap each card. A hard composite area usually has two tidy routes — and olympiad solvers pick whichever gives rounder numbers.

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A peek inside

Two straight lines cross. One angle is 115°. That 115° sits next to a 65° angle on the line, and the 65° is one angle of a triangle whose second angle is 60°. Find the triangle's third angle.

chase it: next-to on the line = 180 − 115 = 65; then the triangle's third angle = 180 − 65 − 60

Try this at home: On a line: two angles sit on a straight line; one is 115°. The other is __

Ready to play and learn?

Start the free interactive lesson, or print the handout for screen-free play.

Start the free lesson →⬇ Download PDF

Part of Math · Stage 6 · S6 on KAVI Academy — a secular, whole-child learning platform for ages 5–12.