In the diagram below, AM = BM = CM and angle BMC + angle A = \(177^\circ.\) Find angle B in degrees.
+128475 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 )
