lesson
Use the whole turn
1 · Learn
Angles around a point sum to 360° when they fill the complete turn without gaps or overlap. Angles on one side of a straight line sum to 180°.
Use the stated arrangement, not appearance alone. Two angles do not automatically add to 180° merely because they are drawn near each other.
Quarter turns are multiples of 90 degrees. Two quarter turns make 180 degrees, three make 270 degrees, and four make 360 degrees. A 270-degree turn is reflex, leaving a 90-degree turn to complete the circle.
2 · Worked example
Two adjacent angles fill a straight angle. If one is 68°, the other is 180 − 68 = 112°.
3 · Your turn
Three angles around a point fill a full turn. Two are 90° and 145°. Find the third.
Check your answer
125°, because 360 − 90 − 145 = 125.
4 · Apply your learning
Draw labelled arrangements and mark which angles fill the whole. Explain the subtraction before measuring as a check.
Adult guidance and safety
Model the calculation or measurement before relying on a procedure. Explain estimates, units and checks. Use a ruler/protractor and suitable diagrams where needed; text examples alone do not establish practical skill or fluency.
Open your writing and drawing pad
Write, draw or show your working. Use a mouse, pen or finger. This pad is not a submitted answer.
Not saved to your account. Download your drawing as PNG and your typed notes as TXT before leaving or refreshing. They are separate files. Do not enter private information.
Open a picture saved on this device to draw on it again. Opening replaces the drawing, but Undo can restore it. PNG only, up to 4 MB and 4096 × 4096 pixels. The picture stays in this browser; it is not uploaded. Paper lines in a saved picture become part of that picture.
Clear the drawing? Your typed notes will stay. You can undo this action.
Your pad is empty.
Open a UTF-8 TXT file from this device, up to 40 KB and 10,000 characters. It stays in this browser. Opening can be undone until you type again. Downloads keep a new copy; they do not change the file you opened.
Replace the notes on this page with the opened file? Download the current notes first if you want to keep them.
Typed notes are not submitted answers.
Check a calculation · Year 5 onward
Use this only when your teacher or adult allows a calculator for the task. Show your thinking first. It does not replace mental or written arithmetic and does not mark your lesson answer.
Practice this lesson
Lesson resources
Browse the available practice activities and worksheets for this lesson.
Your progress