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Equilateral triangle ABC and square  BCDE are coplanar, as shown. What is the number of degrees in the measure of angle CAD?

 Dec 3, 2018
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Note that BC = AC = CD

 

So......in triangle ACD, angle ACD = angle ACB + angle BCD=  60° + 90°  = 150°

 

And since  AC = CD.....then the angles opposite these sides in triangle ACD are also equal

 

So....angle  CAD = angle CDA

 

So....

 

angle CAD + angle CDA + angle ACD = 180

 

angle CAD + angle CAD + angle ACD =  180

 

2angle CAD + 150  = 180

 

2angle CAD = 180 - 150

 

2angle CAD = 30          divide both sides by 2

 

angle CAD = 15°

 

 

cool cool cool

 Dec 3, 2018

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