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In the diagram below, AM = BM = CM and angle BMC + angle A = \(177^\circ.\)  Find angle B in degrees.

 

 Jun 7, 2022
 #1
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Note that  because  CM = MA   then angles  MCA and MAC  are equal......call their value x

 

And because of the Exterior Angle Theorem, angle BMC  = 2x

 

So

 

BMC + angle A  = 177

2x + x  =177

3x  =177

x =177/3   = 59°  = angle A   (and angle C )

 

So angle CMA  = 180  - 2(59)  = 180  - 118  =  62°

 

And since  BM = CM  then angles   CBM and BCM are equal...call their value y

 

And by the Exterior Angle Theorem

 

Angle CMA  = angle CBM  + angle BCM

 

62  =  y  +  y

 

62  =  2y

 

62 / 2  = y  = 31°  =  measure of angle CBM   (angle B )

 

 

cool cool cool

 Jun 7, 2022

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