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Turn, tilt and twist! Discover acute, right, obtuse, straight, reflex and full-rotation angles, and learn to estimate, measure and draw them with a protractor.
Main skills from this lesson
Angles are everywhere - in pizza slices, clock hands, doors that swing open and the corners of every shape. In this unit you'll learn to name, estimate, measure and draw angles like a pro.
A pizza with one slice missing has a reflex angle at the gap!
Look at the clock hands. They make a different angle at different times:
| Angle type | Size |
|---|---|
| Acute | less than 90 degrees |
| Right | exactly 90 degrees |
| Obtuse | 90 degrees to 180 degrees |
| Straight | exactly 180 degrees |
| Reflex | 180 degrees to 360 degrees |
| Complete rotation | exactly 360 degrees |
Math mindset: angles, lines, shapes and patterns help us describe the whole physical world.
A clock shows 3:00 exactly. What type of angle do the hands make?
Look at each angle and decide what type it is by comparing it to 90 degrees and 180 degrees:
An angle that is greater than 90 degrees but less than 180 degrees is called...
Sometimes you can work an angle out by adding known angles. If part of the angle is a right angle (90 degrees) and the rest is 45 degrees, then the whole angle is 90 degrees + 45 degrees = 135 degrees. Look for right-angle corners on grid paper - they give you 90 degrees for free!
90 degrees + 45 degrees = 135 degrees
Math Language: Reflex angles are larger than 180 degrees but less than 360 degrees.
An internal angle measures 100 degrees. What is the reflex angle on the other side?
To draw a reflex angle like 250 degrees with a half-circle protractor:
Math in real life: where have you seen reflex angles? (Pac-Man's mouth, an open laptop past flat, a pizza missing one slice...)
To draw a 250 degree reflex angle, after marking 180 degrees you measure an extra...
Estimating means making a smart guess before measuring. Compare to 90 degrees (a square corner) and 180 degrees (a straight line):
A very narrow wedge that's only a hair wider than a flat line: 5 degrees, 30 degrees, 40 degrees or 15 degrees - which is the best estimate?
A clinometer is a tool that measures the angle of a slope or the height of tall things like trees or buildings without climbing them. Engineers, surveyors and even astronomers use clinometers to measure angles of elevation.
Real life: people use clinometers to check the slope of roofs, hills and roads.
Which type of angle is a reflex angle in Exercise 2 most likely to be - bigger than which value?
Add up the angles drawn inside each shape and you'll spot a pattern:
These sums are always true, no matter the shape!
Triangle = 180 degrees, Quadrilateral = 360 degrees
A triangle has angles 70 degrees, 50 degrees and?. What is the missing angle?
To draw 30 degrees, 68 degrees or 190 degrees with a protractor:
An angle of 268 degrees is what type of angle?
Zainab says the angle measures 50 degrees, but she is wrong. When you read a protractor you must use the scale that starts at 0 degrees on your baseline. Reading the other scale flips your answer. The angle she's looking at is actually 130 degrees - she read the wrong row of numbers (50 degrees and 130 degrees are on the same line because they add to 180 degrees).
Remember: always start counting from the 0 degrees on your baseline!
Two numbers on the same protractor mark are 50 degrees and 130 degrees. They always add up to...
Use a protractor on different triangles and quadrilaterals, then add up their inside angles.
This is a rule you can use forever.
| Shape | Sum of inside angles |
|---|---|
| Triangle | 180 degrees |
| Quadrilateral (square, rectangle, etc.) | 360 degrees |
Three angles of a quadrilateral are 90 degrees, 90 degrees and 90 degrees. What is the fourth angle?
Kiran joined two equilateral triangles. Each angle in an equilateral triangle is 60 degrees because 180 degrees / 3 = 60 degrees. So when two equilateral triangles meet edge-to-edge to form a rhombus:
Each angle in equilateral triangle = 60 degrees
Each angle in an equilateral triangle equals...
Clock hands sweep angles as time passes.
If Neena's class lasted 1 hour, the minute hand turned 360 degrees and the hour hand turned 30 degrees.
Minute hand: 6 degrees / min Hour hand: 0.5 degrees / min
In 30 minutes, how many degrees does the minute hand turn?
Check yourself! Measure each angle with your protractor, then name its type.
Draw these angles accurately: 115 degrees (obtuse), 50 degrees (acute), 93 degrees (obtuse), 70 degrees (acute), 165 degrees (obtuse), 25 degrees (acute). Tip: 90 degrees is the dividing line between acute and obtuse.
What type of angle is 93 degrees?
A great way to improve is to estimate first, then measure:
| Angle | Estimate | Measure | Type |
|---|---|---|---|
| a | ? | ? | ? |
| b | ? | ? | ? |
| c | ? | ? | ? |
Estimating is a skill - it gets sharper with practice.
Think back over the unit:
Angles matter for builders, sailors, athletes, designers and you!
How many types of angles did this unit cover?
Continue with quizzes, flashcards, or games when you are ready.