Thirty-Six

Unit 6 · GeometryG1 · Angles & Polygons · Aerodynamics & Navigation

Angles, Lines & Polygons

Chase vertical, supplementary, parallel-line, triangle, and polygon angles.

  • 30 min
  • Unlocks: Fin Geometry

Ready when you are

7 steps · about 30 minutes

Start with the warm-up.

Start

Step 1 of 7Warm-upDone

Warm-up

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Key terms

supplementary angles
two angles whose measures sum to 180 degrees

Step 2 of 7Try it firstDone

Try it first

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Try this before the explanation. Commit to a setup, even if you are unsure.

Step 3 of 7LearnDone

The big idea

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The decision that matters

Name the angle relationship before writing an equation. Write that decision before calculating. It turns a crowded ACT stem into a familiar structure and makes the likely distractors easier to spot.

Key idea

Structure before arithmetic

Name the angle relationship before writing an equation. Keep exact values through the setup; round only when the stem asks.
Core relationship
S=(n−2)180∘S=(n-2)180^\circ

Use the formula only after matching every symbol to the diagram or equation.

Algebra or Desmos?

Angle relationships create the equation; a calculator only checks the resulting arithmetic. Write whether the angles are equal, supplementary, or part of a polygon sum before entering numbers.

Explore in Desmos

Check an angle sum after building the equation

Desmos is only an arithmetic check here; angle relationships must supply the equation.

The calculator is live: change anything and see what happens.

Check an angle sum after building the equation

Degree mode

Press Escape to leave the calculator (twice if a menu is open).

Loading Desmos…

Trap

The main trap

Parallel-line angle rules require an actual parallel marking or statement.

Step 4 of 7Worked examplesDone

Worked examples

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Skip check · 2 questions

Already know this? Get both right on the first try and you can skip the worked examples.

Worked example

Example 1

Problem

Two supplementary angles measure 3x+123x+12 and 5x−85x-8. Find xx and both angle measures.
Set their sum to 180.

Which equation follows from the word supplementary?

The angles are 78∘78^\circ and 102∘102^\circ.

Which check confirms they are supplementary?

Worked example

Example 2: ACT twist

Problem

Find each interior angle of a regular 15-gon.
Interior sum is 13(180)=234013(180)=2340.
The total interior-angle sum is 2340∘2340^\circ.

Which quantity must be divided by 15?

Each angle is 156∘156^\circ.

Why is division by 15 justified?

Faded example · you finish it

Example 3: You finish it

Problem

A triangle has angles 2x2x, 3x+103x+10, and 5x−205x-20. Find xx.
10x−10=18010x-10=180

Solve 10x−10=18010x-10=180.

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Practice

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Step 6 of 7Spot the mistakeDone

Spot the mistake

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Spot the mistake

Where did it go wrong?

One line has an error. Click the line where it first goes wrong.

Step 7 of 7Exit ticketDone

Exit ticket

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Optional · 4 questions · Hardest levelChallenge set: the kind of question that decides a 36

These are last-ten-questions hard. Take your time, use Desmos when it helps, and expect to miss some: that's where the learning is.