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In the figure AB = BC, CD = BD, and angle CAD = 70. What is the measure of angle ADC?

Guest Jun 19, 2014

Best Answer 

 #1
avatar+576 
+5

This question is based on recognition of isosceles triangles, meaning exactly two legs of the triangle are congruent(the same length).  Based on the fact that AB=BC we know that triangle ACB is isosceles which means it's base angles are congruent.  Since angle CAD=70 we can be certain that angle ACB=70. 

The sum of the interior angles of the triangle is 180 so 180-70-70=40=angle B.  Now we look at triengl CDB which is isosceles because CD=BD.  Therefore, base angles are congruent which tells us angle BCD=40. 

 

Since angle ACB=70 and angle BCD=40, angle ACD=30 because 30+40=70 as ACD+BCD=ACB

 

Focusing on triangle ACD now we see that we have angles of 30 and 70.  Since the triangles angles sum to 180 that leaves 80 degrees left over for angle ADC. 

 

ADC=80

jboy314  Jun 19, 2014
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3+0 Answers

 #1
avatar+576 
+5
Best Answer

This question is based on recognition of isosceles triangles, meaning exactly two legs of the triangle are congruent(the same length).  Based on the fact that AB=BC we know that triangle ACB is isosceles which means it's base angles are congruent.  Since angle CAD=70 we can be certain that angle ACB=70. 

The sum of the interior angles of the triangle is 180 so 180-70-70=40=angle B.  Now we look at triengl CDB which is isosceles because CD=BD.  Therefore, base angles are congruent which tells us angle BCD=40. 

 

Since angle ACB=70 and angle BCD=40, angle ACD=30 because 30+40=70 as ACD+BCD=ACB

 

Focusing on triangle ACD now we see that we have angles of 30 and 70.  Since the triangles angles sum to 180 that leaves 80 degrees left over for angle ADC. 

 

ADC=80

jboy314  Jun 19, 2014
 #2
avatar+85564 
0

Aw heck, jboy314, you beat me to it!!!

 

Thumbs up and a good answer, too....points as well!!

 

CPhill  Jun 19, 2014
 #3
avatar+19191 
0
  1. ABC=180-2*70         =   40
  2. ADC=2*ABC             =   80
heureka  Jun 20, 2014

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