M12 | Maths Made Easy


Question: ABCD is a quadrilateral. Find the missing angle marked x.


Answer: This is a 4-sided shape, which we now know has interior angles that add up to 180\times 2=360. So, if we know all the interior angles other than x, then we can find x.

Currently we don’t know them all, however we do have an exterior angle, and we know that exterior angles form a straight line with their associated interior angles, we get the interior angle at D to be 180 - 121 = 59\degree.

Now we know all 4 interior angles, we get that

x = 360 - 84 - 100 - 59 = 117\degree.

You will find algebra involved more in questions on this topic, but as long as you know what the interior and exterior angles add up to then you can write the statement “these angles add up to ___” as an equation which you can then solve.