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1. In the diagram below, AM=BM=CM and BMC+A=201. Find B in degrees.

 

2. In the diagram, BDF and ECF have the same area. If DB=2,BA=3, and AE=4, find the length of ¯EC.

 

3. In triangle ABCAB=AC, ABC=72, and segment ¯BD bisects ABC with point D on side ¯AC. If point E is on side ¯BC such that segment ¯DE is parallel to side ¯AB and point F is on side ¯AC such that segment ¯EF is parallel to segment ¯BD, how many isosceles triangles are in the figure shown? 

 Feb 11, 2021
 #1
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You are only allowed to ask one question at a time.

 Feb 11, 2021
 #2
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1/   ∠MCA  ≅ ∠A      (These angles are 21º larger than  ∠AMC )

 

∠BMC + ∠AMC = 180º

 

 ∠AMC = 1/3(180 - 42) = 46º

 

 ∠BMC = 180 - 46 = 138º

 

 ∠B = 1/2(180 - 138) = 21º 

 

  

 Feb 11, 2021
edited by jugoslav  Feb 11, 2021
 #3
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its wrong

Guest Feb 12, 2021
 #4
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You are right! Angle B = 23 degrees  

jugoslav

Dragan  Feb 14, 2021

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