Angles and Lines

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 \(y\)?

(Assume the pencils have a rectangular body and have their tips resembling isosceles triangles)

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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