If the length of a diagonal of a rectangle is twice the length of one of the sides of this rectangle, then what are the angle measurements between the diagonals?

Answer:The angle measurements between the diagonals are 60° and 120°Step-by-step explanation:LetD -----> the diagonal of rectanglex -----> the length of rectangley ----> the width of rectanglewe know thatApplying the Pythagoras Theorem[tex]D^2=x^2+y^2[/tex] -----> equation A[tex]D=2x[/tex] ----> equation Bsubstitute equation B in equation A[tex](2x)^2=x^2+y^2[/tex][tex]4x^2=x^2+y^2[/tex][tex]y^2=3x^2[/tex][tex]y=x\sqrt{3}[/tex]see the attached figure to better understand the problemThe triangle DOC is an isosceles trianglem∠ODC= m∠OCDFind the measure of angle m∠ODCtan(∠ODC)=y/xRemember that[tex]y=x\sqrt{3}[/tex]substitutetan(m∠ODC)=x√3/xtan(m∠ODC)=√3m∠ODC=arc tan(√3)m∠ODC=60°m∠OCD=60°Find the measure of angle m∠DOCRemember that the sum of the internal angles of triangle must be equal to 180 degreesThe triangle DOC is an isosceles trianglem∠ODC= m∠OCDsom∠ODC+ m∠OCD+m∠DOC=180°substitute the given values60°+ 60°+m∠DOC=180°120°+m∠DOC=180°m∠DOC=180°-120°=60°Remember that the angle measurements between the diagonals are m∠DOC and m∠BOCThe sum of the angle measurements between the diagonals is equal to 180 degrees, because are supplementary angles (form a linear pair) we havem∠DOC=60°som∠BOC=120°thereforeThe angle measurements between the diagonals are 60° and 120°