Question

HELP ME PLEASE DB is a diagonal of parallelogram ABCD, what is the measure of ADB

Answer 1

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

Answer 2

m < DAB + m < ADC = 180 (because ABCD is a parallelogram)

so m < ADC = 180 -112 = 68 degrees

Therefore m < ADB = 68 - 27 = 41 degrees (answer)