The picture hands you the equation: a corner is 90, a straight line is 180, a triangle is 180, and angles across an X are equal. Then which three lengths can close into a triangle, when the conditions give one triangle, many or none, and how a scale drawing multiplies every length by one number and leaves every angle alone. Study cards, hints, a practice quiz at three levels, and four workshop activities that check themselves.
A straight line is 180. One of these angles is 130. You already know the other one.
Four facts do most of this unit. A corner is 90 — complementary. A straight line is 180 — supplementary. A triangle is 180. Angles across an X are equal.
Four things people get wrong
⚠️People often think…
Complementary and supplementary are pretty much the same thing.
Complementary adds to 90. Supplementary adds to 180. Mixing them up is the single most common slip on this test.
C is for Corner, 90. S is for Straight, 180.
⚠️People often think…
Angles across an X add up to 180.
Angles straight across from each other are EQUAL. Set them equal to each other. The pairs that add to 180 are the ones side by side.
Across: equal. Side by side: 180.
⚠️People often think…
Solving for x is the answer.
If the question asks for the ANGLE, x is only halfway. Put x back into the expression and finish. An angle labeled 2x + 10 with x = 35 is 80, not 35.
Found x? Reread what was asked.
⚠️People often think…
Any three lengths can make a triangle.
The two short sides have to add to MORE than the long side. Exactly equal is not enough — that lies flat and never closes.
Add the two short ones. More, not equal.
Read the picture, write the equation
1Watch one
Two angles sit on a straight line. One is 118°. Find the other.
A straight line means 180.
The two angles add to 180.
180 − 118 = 62.
The other angle is 62°.
2Do one with me
A triangle has angles of 40° and 75°. Find the third.
A triangle adds to
40 + 75 =
180 − 115 =
💬One sentence, then you move on
Why is knowing two angles of a triangle always enough?
3Try one
Can sides of 4, 5 and 10 close into a triangle? Write yes or no.
I want a hint first
Add the two short sides. Is 4 + 5 more than 10?
💬Last one — then you're done here
How do you check whether three lengths can make a triangle?
Where this goes
Where this lives
A roof pitch, a wheelchair ramp, a floor plan. A scale drawing multiplies every length by one number and leaves every angle exactly alone.
What this feeds
Next unit is probability and sampling, where the answer is how likely something is rather than how big it is.
Find one right angle and one straight angle in the room you are in.
One card at a time — tap “Show me” to check yourself, then Next. Start at Foundation; when those feel easy, climb.
Helpful Hints
🪜 From a picture to an equation — the ladder
Find the relationship in the picture (a corner? a straight line? an X? a triangle? a full turn?) → write its total (90, 180, equal, 180, 360) → put the angle expressions in → solve for x → put x BACK to get the angle → check that the pieces add up.
Spot it, total it, write it, solve it, plug it back.
🤝 The whole topic in one idea
Geometry gives you the equation for free. A corner is 90, a straight line is 180, a triangle is 180, a full turn is 360, and angles across an X are equal. A scale drawing is the same idea for lengths: every length is multiplied by ONE number, and every angle stays exactly as it was.
⚠️ Traps the test loves
Complementary is 90 (C for Corner). Supplementary is 180 (S for Straight). Mixing them is the #1 slip.
Solving for x is not the end. If the question asks for the ANGLE, put x back in.
Vertical angles are EQUAL — set them equal, do not add them to 180.
Triangle inequality: the two SHORT sides must add to MORE than the long side. Equal is not enough — that is a flat line.
Three angles fix the SHAPE, not the size: many triangles. Three sides fix both: one triangle.
Area does not use the scale factor — it uses the scale factor SQUARED.
📐 Angle relationships — the chart
Name
Looks like
Equation
Complementary
two angles filling a square corner
a + b = 90
Supplementary
two angles along a straight line
a + b = 180
Vertical
across from each other in an X
a = b
Triangle
the three inside angles
a + b + c = 180
Around a point
a full turn
sum = 360
🎯 How the test will ask
A picture with an expression like (3x + 10)° — “find x” or “find the angle.” Read which.
Three lengths — “can these make a triangle?” (add the two shortest).
A list of conditions — “one triangle, more than one, or none?”
A map or floor plan — drawing to real (multiply) or real to drawing (divide).
A scale drawing and an AREA — find the real lengths first, then multiply them.
“Redraw at a different scale” — go through the real size, or compare the two scales.
✅ Before the test, can you…
Name complementary, supplementary, vertical and adjacent angles in a picture?
Write and solve an equation for an unknown angle — and plug x back in?
Find a triangle’s third angle, and classify the triangle?
Decide whether three lengths make a triangle, and give the range for a third side?
Go from a scale drawing to real lengths and back?
Explain why real area uses the scale factor squared?
Pick your level
Look back at anything you missed — the hint that appeared is exactly what to reread tonight.
How sure did you feel?
Workshop
Work like a mathematician: name the angle pairs, test which lengths close into a triangle, read a protractor and then scale the drawing, then settle an argument about a poster. Every activity checks itself, and hints are free.
Your practice never leaves this device. There is no account and no sign-in. Your work is saved in this browser only, and you can erase it whenever you want.
Your practice record — saved on this device
This is your record of the module on screen — it stays here and goes nowhere. Independent means you got it right on the first tap; supported means you got it after the explain-and-retry, or marked ‘I had it’ on a revealed answer. Both count, and neither is a grade. If your teacher asks, copy the row or show them this screen.
Date
—
Topic
—
Level
—
Independent
0 of 0
Supported
0 of 0
Hints used
0
Cards studied
0
Lab
—
Traps met
0
Explained in own words
0
Confidence
—
The answer key is for a teacher: it prints only from here, for the unit on screen. Print the study packet prints the study pages and a blank quiz — never the answers.