Question

PLEASE PLEASE HELP ASAPIn parallelogram ABCD, AD=19, EC=15, mABC=66°, mDAC=78° and mBDC=19°.Find mDAB.

Answer 1

the measures of the opposite angles of a parallelogram are equal

so

`\text{ADC}=\text{ABC}`

and

`DAB=\text{BCD}`

the sum of the total angles of a parallelogram is 360

so

`\text{ADC}+\text{ABC}+\text{DAB+BCD=}360`

where ABC=ADC=66

and

BCD=DAB

so replacing

`\begin{gathered} 66+66+\text{DAB}+\text{DAB}=360 \\ 132+2\text{DAB}=360 \end{gathered}`

now solve DAB

`\begin{gathered} 2\text{DAB}=360-132 \\ \text{DAB}=(228)/(2) \\ \text{DAB}=114 \end{gathered}`

the measure of DAB is 114°