Please find the attached file and look at the diagram of a

triangle.

As you can see, we need to find the size of the

angle marked "x" (i.e. angle DEF).

You can identify the sizes of surrounding angles using your basic knowledge of geometry as follows:

Angle ACD = 20 (Angle sum of triangle = 180)

Angle AFB = 50

(Angle sum of triangle = 180)

Angle DFE = 50 (Opposite angles are equal in size)

Angle AFD = 130 (Angles on a straight line add up to 180)

Angle BFE = 130

(Opposite angles are equal in size)

Angle ADB = 40

(Angle sum of triangle = 180)

Angle AEB = 30

(Angle sum of triangle = 180)

But how can it possible to find out the size of the angle DEF?

Honestly, I am stuck and cannot see any way to find it out.

The diagram on the file is drawn to scale, so I actuallly measured the angle DEF to see the size of it, then I found that it is exactly 20 degrees, therefore, the answer must be 20.

If so, the triangles EDC and FEB are similar, however, I cannot find any way to prove that they are similar only with these pieces of information on the diagram without measuring the angle using a protractor.

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