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 yy (ACD\angle ACD) in the diagram. If the angle of the pencil tip AA is 4040^\circ and the angle of the pencil tip ECDECD is 3030^\circ, then what is the value of yy?

(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 A+B+C \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 xx in degrees.

In the figure above, ABCABC and CDECDE are equilateral triangles. Find ADE\angle ADE in degrees.

Source: HKCEE 1991 #51.


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