Examine the diagram. It is not drawn to scale. A triangle has angles A, C, 57 degrees. The exterior angle to angle A is B and the exterior angle to angle C is 118 degrees. Use the measurements provided in the diagram to determine the measure of AngleB. mAngleB = °

To find the measure of Angle B, we can use the exterior angle theorem, which states that the measure of an exterior angle is equal to the sum of the measures of the two opposite interior angles. Given: Angle A = \( m A \) Angle C = \( m C \) Exterior angle B = 118 degrees From the exterior angle theorem: \[ m B = m A + m C \] We also know that the sum of the angles in a triangle is 180 degrees: \[ m A + m C + 57^ = 180^ \] This can be rearranged to find \( m A + m C \): \[ m A + m C = 180^ - 57^ = 123^ \] Now, substituting this into the equation for Angle B: \[ m B = 123^ \] Thus, the measure of Angle B is: \[ m B = 123^ \]