Find angle X
Geometry
Level
pending
The triangle ABC has a D point in the side AB, so that AB = CD. Also in the figure, the angle ABC = 100º and the angle BCD = 40 °.
Get the measure of ACD = x angle.
The answer is 10.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
Take an auxiliary triangle, BCE, equilateral. With this the DCE angle becomes 100 ° and gain congruence between triangles ABC ~ DCE (Case LAL): Sides (EC = BC), Angles (DCE =ABC = 100 °) and Sides (AB = CD)
That congruence, we have @ACB = DEC = 40 + x.
Note that CBD = 40 ° angle (@DBC + @BCD + @CDB = 180° ,so, 100° + 40º + @CDB = 180° and it follows that CDB = 40 °). Thus the triangle is isosceles BDC (DB = BC).
As an equilateral triangle, BC = BE, and triangle DBC: DB = BC, we have DB = BE. The BDE is also triangle is isosceles with @BDE = @BED = 10 °.
If @BEC = 60 ° + 40 = 10 + x it follows that x = 10 °.
OBS. @ Here meant "angle".