Myriora Maths › Maths foundations › Chapter 15: Shape and space
Angle facts
Ages 9–11Chapter 15 · Lesson 4✓ Watched
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Practise
Ten new questions every time. Answer them all, then check: you get your score, and the working for anything you missed.
In this lesson
- Angles on a straight line add up to a hundred and eighty degrees.
- Angles round a point add up to three hundred and sixty.
- Angles in a triangle add up to a hundred and eighty.
- And angles in a quadrilateral add up to three hundred and sixty.
Your turn
Three angles of a quadrilateral are ninety, ninety and a hundred degrees. What is the fourth?
Show the answer
Ninety add ninety add a hundred is two hundred and eighty. Three hundred and sixty take away two hundred and eighty is eighty degrees!
The common mistake
Here's a question that catches lots of people. A triangle has angles of ninety and forty degrees. What is the third angle? Some people take both away from three hundred and sixty, and get two hundred and thirty. But that's bigger than the whole triangle! A triangle's angles add up to a hundred and eighty, so it's fifty degrees.
Try it at home
Tear the three corners off a paper triangle and line them up to make a straight line.
Read the whole lesson
Hello, and welcome to Myriora Maths! If you know just a few angle facts, you can work out angles without measuring them. Let's learn four of them.
Angles on a straight line add up to a hundred and eighty degrees. So if one angle is a hundred and ten degrees, the other is a hundred and eighty take away a hundred and ten: seventy degrees.
Angles all the way round a point add up to three hundred and sixty degrees, a full turn. Ninety, a hundred and twenty and eighty make two hundred and ninety. So the missing angle is seventy degrees.
The three angles in a triangle always add up to a hundred and eighty degrees. Here's why: tear off the corners, and put them together. They make a straight line!
A four-sided shape can be cut into two triangles. So the angles in a quadrilateral add up to two lots of a hundred and eighty: three hundred and sixty degrees.
Let's try one together. A triangle has angles of fifty and sixty degrees. What is the third angle? Say it out loud!
Fifty add sixty is a hundred and ten. A hundred and eighty take away a hundred and ten is seventy degrees!
Here's a question that catches lots of people. A triangle has angles of ninety and forty degrees. What is the third angle? Some people take both away from three hundred and sixty, and get two hundred and thirty. But that's bigger than the whole triangle! A triangle's angles add up to a hundred and eighty, so it's fifty degrees.
Your turn! Three angles of a quadrilateral are ninety, ninety and a hundred degrees. What is the fourth? Pick the right card. You've got twenty seconds, or pause the video. Go!
Time's up! Ninety add ninety add a hundred is two hundred and eighty. Three hundred and sixty take away two hundred and eighty is eighty degrees!
Quick review. Angles on a straight line add up to a hundred and eighty degrees. Angles round a point add up to three hundred and sixty. Angles in a triangle add up to a hundred and eighty. And angles in a quadrilateral add up to three hundred and sixty. See you next time!