In parallelogram EFGH , EJ=x2−4 and JG=3x .What is EG ?461224What is the measure of ∠DAB?Enter your answer in the box.

Accepted Solution

we know thatIn a parallelogram; opposite sides are equal, opposite angles are equal and diagonals bisect each other.soPart 1) In this problem[tex]EG=EJ+JG[/tex][tex]EJ=JG[/tex] -----> remember diagonals bisect each othersubstitute the values[tex]x^{2} -4=3x[/tex][tex]x^{2} -3x-4=0[/tex]Using a graphing tool-------> solve the quadratic equationsee the attached figureThe solution is[tex]x=4[/tex]Find the value of EG[tex]EG=2JG[/tex][tex]EG=2*3*4=24\ units[/tex]thereforethe answer Part 1) is[tex]EG=24\ units[/tex]Part 2) What is the measure of ∠DAB?we know that∠DAB+∠ADC=[tex]180\°[/tex] ------> by consecutive interior anglesin this problem we have∠ADC=[tex]96\°[/tex]substitute∠DAB=[tex]180\°-96\°[/tex]∠DAB=[tex]84\°[/tex]thereforethe answer Part 2) is ∠DAB=[tex]84\°[/tex]