M and N are the midpoints of sides AC and CB of triangle ABC. Find AB and ∠B if MN = 8 cm, ∠CNM = 46 °.

Since M is the middle of the AC side (by condition) and N is the middle of the BC side (by condition), then MN is the middle line of the ABC triangle, parallel to the base of AB. The middle line is half the size of the base.

Hence, AB = MN * 2 = 8 * 2 = 16 cm.

Since the centerline is parallel to the base, angle B and angle CNM are corresponding when MN and AB and secant BC are parallel. Hence, the angle B = angle CNM = 46 °.

Answer: AB is 16 cm, angle B is 46 °.

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