[Closed] Y6 Maths "Angles in Polygons"

Its maths Jim, but not as we know it...

the teacher is wrong

A quadrilateral always has 4 right angles? Say what!?

I think the idea behind this is to divide the polygons into triangles. Each time you add a side (triangle to quadrilateral, quadrilateral to pentagon, etc), you add another 180 degrees to the total.

The right angles thing is wrong, plain and simple, because the teacher doesn't understand the subject. You understand it because you've spotted the mistaken assumption that dividing the total of the interior angles by 90 degrees gives you an answer in "right angles".

Primary school teachers aren't maths teachers. The way this exercise should be set is to look at dividing the polygons into triangles, at which point you observe that the total angle in the shape is equal to the (number of sides - 2) * 180.

The final one is total sum of angles

ie the sum and the rule is a triangle has 2x90=180 as a total. The angles can obviously not be 90 + 90 but a right angle triangle has 1 x 90deg and the other two angles add up to 90 deg to form the 2 x 90 deg.

If one angle is 178 deg then the other two must add up to 2 deg.

In a quadrilateral the sum is 360 deg which is 4 x 90 deg. could be 100 + 80 twice but will still be 360.

I think the teacher is just demonstrating the rule in a confusing way but is doing to to demonstrate the pattern which will relate to 90 deg angles. A pentagon will follow the rule and be 6 x 90.

Personally I would say a triangle is 1 x 180, a quadrilateral is 2 x 180 and a pentagon is 3 x 180 etc etc. But maybe they find sticking to 90 deg less confusing.

Wysiwyg at least you can draw a quadrilateral with 4 right angles, I'm interested in this triangle with 2

poor description, but teacher seems to be using "2 right angles" as some sort of shit shorthand for 180 degrees of total internal angles (why it should be easier to say 2x90 rather than 1x180, I dunno)

They traditionally teach that you split a shape into triangles and these each add 180 to the total

so traingle has 1 triangle = 180
quadrilateral has 2 = 360
pentagon, 3 = 540

etc

(n-2)x180

poor description, but teacher seems to be using "2 right angles" as some sort of shit shorthand for 180 degrees

Yeah, maybe it's to help visualise the angles. "270 degrees" is meaningless at first, whereas "three right angles" is immediately accessible. It's a bit weird though.

thepurist - Member
Wysiwyg at least you can draw a quadrilateral with 4 right angles, I'm interested in this triangle with 2

This is simple conceptual physics, a triangle is a three sided shape which satisfies a series of rules. Draw one on a sphere and in the context of the sphere the triangle is two dimensional. Extrapolate that same triangle onto a plane which is flat and it ceases to conform to several of the rules which you consider make it a triangle, it's still planar, still has three sides but no longer has angles which sum to 180degrees, and the sides don't appear straight but, it is clearly still a triangle at the same time. Frankly I'm amazed they don't teach this stuff at an earlier age.

Got it!

Thanks, and a virtual shandy from the lad to you all 🙂

Dangerous brain - you're talking about non-Euclidean geometry. I think that only comes up in year 7 🙂

I always liked that puzzle:

"How can you walk south for a mile, then east for a mile and then north for a mile and end up exactly where you started"