**Complex shapes**

Looking at another example, we have a more complex shape and we are asked to find the value of the angle CED.

To do this we need to solve some intermediate angles along the way, which is usually what you will need to accomplish when solving angles.

With the information given we can first find angle EBC = 180°-123° = 57° (reasoning is “angles on a straight line add to 180 degrees”)

**A possible question **

in the diagram below ABCD is a straight line. Fine the value of angle CED.

Next we can find angle ECB = 78° (reasoning is “angles in a triangle add to 180”)

Then angle ECD = 102° (reasoning is “angles on a straight line”)

We are finally in a position to calculate the desired angle, CED. We methodically found angle after angle as new information was garnered until we reached our solution.

CED = 41° (reasoning is “angles in a triangle add to 180”).