Apart from knowing all the geometrical relationships and properties that we have already covered: (quadrilaterals, triangles , angles and parallel lines ) there are a number of strategies you can use to solve more complex geometrical angle and length problems.

start with a sketch and fill in everything that you know, by applying the rules you know one a time. You will gradually work towards the final solution - it may be a longer route, but you will still get there in the end
Have a look at identifying a path from information you are given to the pronumeral you are trying to find, sometimes this gives you an idea about the angles you may need to find along the way
If all else fails, look at the information you are given and work through some of the most common rules first, X, U, Z, F and see if using either of those rules helps you towards the pronumerals you are trying to find.

Let's have a look at these techniques in action with some worked examples.

Examples

Question 1

$B$B is the centre of the circle shown.

Find the value of $x$x, giving reasons for your answer.

Question 2

Calculate $x$x, giving reasons for your answer.

Question 3

Calculate $x$x giving reasons for your answer.

Outcomes

9.G.Q.1

The diagonal divides a parallelogram into two congruent triangles. In a parallelogram opposite sides are equal and conversely. In a parallelogram opposite angles are equal and conversely. A quadrilateral is a parallelogram if a pair of its opposite sides is parallel and equal. In a parallelogram, the diagonals bisect each other and conversely.

Geometrical Calculations