# In an isosceles triangle of ABC, AB=BC, AM bisector is carried out. On continuation of the party of CB for a point of B F point is chosen. It is known that a corner ABF=84 °. Find AMB corner size in degrees. Help please 54
1) Let's find a corner AVS. It will be equal 180 ° - 84 ° = 96 °. 2) Now we need to calculate to what corners at the basis are equal to an isosceles triangle to AVS (a corner YOU and a corner of VSA). We know that they are equal. Also we know that the sum of corners is equal in a triangle 180 °. Let's find a corner at the basis of an isosceles triangle: Let's designate a corner at the basis by a letter "and " for convenience of the decision. Then 2a = 180 ° - 96 ° 2a = 84 ° and = 42 ° So the corner at the basis of a triangle of AVS is equal 42 °. 3) Knowing BAC (42 corner °) we find BAM (42 corner °: 2=21 °) 4) Knowing sizes of two corners of a triangle to YOU we will calculate AMV corner size: 180 ° - 96 ° - 21 ° = 63 ° Answer: AMV corner = 63 °
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