The sum of the measures of the interior angles of a polygon of n sides is
180(n - 2)
A parallelogram has 4 sides, so n = 4.
The sum of the measures of the interior angles of a parallelogram (and all quadrilaterals) is
180(4 - 2) = 180 * 2 = 360
Also, opposite angles of a parallelogram are congruent.
Angles A and C are congruent, so m<A = m<C = 112
m<ADC = m<ABC since they are opposite angles.
m<ADC + m<ABC + m<A + m<C = 360
m<ADC + m<ADC + 112 + 112 = 360
2m<ADC = 136
m<ADC = 68
m<ADB + m<BDC = 68
m<ADB + 27 = 68
m<ADB = 41
