**Subtended **is a funny word, isn't it?

But what does it mean? We see complicated words a lot in maths and it often confuses, and makes things seem more complex, than they actually are.

**Subtended** is the word used to describe the angle made when lines are ** drawn from each end of the diameter of a circle**.

If we look at the diagram below, we can see that the subtended angle created by the diameter is a** right angle**:

It is also positioned within a **semi-circle**, rather than the whole circle.

**Every angle**, which touches both edges of the circumference and that is subtended by the diameter of a semi-circle, is a **right angle**.

This sounds complex, but all it means is that if you draw a straight line from each end of the diameter to hit the circumference of the circle, the point where they touch will create a right angle.

__Example__

**Find the value of angle x in the diagram below:**

We know that the total angles in a triangle add up to **180°**.

We also know that the one angle of this triangle is a **right angle (90°)**.

We have been given one other angle (**38°**).

If we put these facts together, we can subtract the two known angles from 180° to find x:

180 - 90 - 38 = **52°**

A quick tip before we start, circle theorem questions rarely show the right angle depicted by the square in the corner. Instead, it will be assumed that you **know **that angles subtended from the diameter will create 90°.

In this activity, we will find the value of unknown angles and solve problems requiring the application of the theory explained above.