Quadrilaterals
A quadrilateral is a four-sided shape. It could be a square, rectangle, kite, rhombus, parallelogram or trapezium.
For any quadrilateral, the angles of the four corners add up to \(360^\circ\).
Example
For this rectangle we are given an angle of \(70^\circ\). What is the value of \(x^\circ\)?
Answer
We can work out the value of \(x^\circ\) as follows:
The other angle of the right angle must be \(20^\circ\).
The triangle at the top is isosceles so there is another angle of \(20^\circ\).
The three angles in a triangle add up to \(180^\circ\)
So \(20+20=40\)
\(180-40=140\)
Therefore \(x^\circ=140\)
Now try the example questions below.
Question
For this kite we are given an angle of \(40^\circ\). What is the value of \(y^\circ\)?
We can work out the value of \(y^\circ\) as follows:
The diagonals meet at right angles so we know we have an angle of \(90^\circ\).
The three angles in a triangle add up to \(180^\circ\).
So we must have an angle of \(50^\circ\) in the top left triangle.
The long diagonal is a line of symmetry so \(y^\circ = 50^\circ\)
Question
Calculate \(x^\circ\) on the following kite.
As we know this is a kite, we then know from the properties of a kite that the angle opposite \(87^\circ\) is also \(87^\circ\).
So we can work out \(x^\circ\) as follows:
\(87^\circ+87^\circ+52^\circ=226^\circ\)
\(360^\circ-226^\circ=134^\circ\)
\(x^\circ=134^\circ\)
More guides on this topic
- Determine the gradient of a straight line
- Circle geometry
- Calculating the volume of a standard solid
- Applying Pythagoras Theorem
- Using similarity
- Working with two-dimensional vectors
- Working with three-dimensional coordinates
- Using vector components
- Calculating the magnitude of a vector
- An Approximate History of Co-ordinates