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1. In the diagram below, \(AM=BM=CM\) and \(\angle BMC+\angle A = 201^\circ.\) Find \(\angle B\) in degrees.

 

2. In the diagram, \(\triangle BDF\) and \(\triangle ECF\) have the same area. If \(DB=2,BA=3,\) and \(AE=4,\) find the length of \(\overline{EC}.\)

 

3. In triangle \(ABC\)\(AB=AC,\) \(\angle ABC=72^{\circ},\) and segment \(\overline{BD}\) bisects \(\angle ABC\) with point D on side \(\overline{AC}.\) If point E is on side \(\overline{BC}\) such that segment \(\overline{DE}\) is parallel to side \(\overline{AB}\) and point F is on side \(\overline{AC}\) such that segment \(\overline{EF}\) is parallel to segment \(\overline{BD},\) 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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