What is the sum of all the angles in a 4 sided shape (angles in a quadrilateral add up to 360 degrees)
Angle In A Quadrilateral Add To 360 Video
Angles in a quadrilateral add up to 360⁰. This is because you can divide up a quadrilateral into 2 triangles and since the angles in a triangle add up to 180⁰, then 2 × 180⁰ = 360⁰. So if you are asked to find a missing angle in a quadrilateral, find the total of the 3 angles that are already given and subtract this total off 360⁰.
Work out angle x in this quadrilateral.
First of all work out the total of the 3 angles that are given:
44 + 124 + 65 = 233⁰
All you need to do now is take this total off 360⁰
360 – 233 = 127⁰.
Work out angle y in this trapezium.
Again, find the total of the 3 angles that are given. Also, make sure you count the 2 right angles that are 90⁰ each. So:
126 + 90 + 90 = 306⁰
All you need to do next is take this total off 360⁰
360 – 306 = 54⁰.
Four angles in a quadrilateral have angles equal to 3x + 6, 2x + 3, x + 11 and 4x. Calculate the size of all of the angles in this quadrilateral.
Let’s begin by adding up the 4 angles that are given. This will give us another expression.
3x + 6 + 2x+ 3 + x + 11 + 4x
Now simplify this expression (add the x terms together and the numbers together)
= 10x + 20
As shown above the angles in a 4 sided shape add up to 360⁰, so you can make an equation involving x:
10x + 20 = 360.
If you know solve this equation you will be able to find the value of x.
10x + 20 = 360 (take 20 off both sides)
10x = 340 (divide both sides by 10)
x = 34⁰.
Finally, if you substitute x = 34 into the 4 expressions above this will give the size of all the angles.
3x + 6 = 3 × 34 + 6 = 108⁰
2x + 3 = 2 × 34 + 3 = 71⁰
x + 11 = 34 + 11 = 45⁰
4x = 4 × 34 = 136⁰
You can check that these 4 angles are the correct size by seeing if they sum to 360⁰.
108 + 71 + 45 + 136 = 360⁰.
So these 4 angles are the correct size.
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