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Geometry

# Angles and Lines: Level 2 Challenges

Hazri prepared another two pencils and he aligned them as shown in the diagram above.

The two pencils form an angle which is labelled $$y$$ ($$\angle ACD$$) in the diagram. If the angle of the pencil tip $$A$$ is $$40^\circ$$ and the angle of the pencil tip $$ECD$$ is $$30^\circ$$, then what is the value of $$y$$?

Three squares are joined together as shown in figure to create a triangle.

What is the sum of angles $$\angle A + \angle B + \angle C$$ ?

Note: We are referring to the "exterior angles", not the interior angles of the triangle.

As shown in the diagram above, there lie 3 squares between 2 parallel lines such that each pair--(line, square) or (square, square)--just meet at a vertex. Find the measure of angle $$x$$ in degrees.

In the figure above, $$ABC$$ and $$CDE$$ are equilateral triangles. Find $$\angle ADE$$ in degrees.



###### Source: HKCEE 1991 #51.

Is it possible to cut this obtuse triangle into pieces so that every piece is an acute triangle?

My failures so far ...

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