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In the diagram below, B, C, and D are all on the same line, angle BAC =24 degrees and AB = AC = CD

If angle ADC = x degrees, what is the value of x?

 

Guest Nov 28, 2017
edited by Guest  Nov 28, 2017

Best Answer 

 #1
avatar+7266 
+2

The sum of the angles in every triangle  =  180°  , so

∠ABC + ∠ACB + 24°  =  180°

                                                  AB = AC , so triangle  ABC is isoscelese and ∠ABC = ∠ACB .

∠ACB + ∠ACB + 24°  =  180°   Subtract  24  from both sides.

∠ACB + ∠ACB  =  156°            Combine like terms.

2∠ACB  =  156°                        Divide both sides of the equation by  2 .

∠ACB  =  78°

 

Since  B, C, and D  are on the same line...

∠ACB + ∠ACD  =  180°

78° + ∠ACD  =  180°

∠ACD  =  102°

 

And triangle ACD is also isoscelese with  ∠CAD = ∠ADC = x   So...

x + x + 102°  =  180°

2x  =  78°

x  =  39°

hectictar  Nov 28, 2017
 #1
avatar+7266 
+2
Best Answer

The sum of the angles in every triangle  =  180°  , so

∠ABC + ∠ACB + 24°  =  180°

                                                  AB = AC , so triangle  ABC is isoscelese and ∠ABC = ∠ACB .

∠ACB + ∠ACB + 24°  =  180°   Subtract  24  from both sides.

∠ACB + ∠ACB  =  156°            Combine like terms.

2∠ACB  =  156°                        Divide both sides of the equation by  2 .

∠ACB  =  78°

 

Since  B, C, and D  are on the same line...

∠ACB + ∠ACD  =  180°

78° + ∠ACD  =  180°

∠ACD  =  102°

 

And triangle ACD is also isoscelese with  ∠CAD = ∠ADC = x   So...

x + x + 102°  =  180°

2x  =  78°

x  =  39°

hectictar  Nov 28, 2017

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