Question

I need help with this please. I have tried multiple times but still could not get the correct answers

Answer 1

Recall that the diagonals of a rhombus are perpendicular bisectors of each other, therefore all the right triangles formed by the diagonals as shown in the given diagram are congruent, therefore:

`\begin{gathered} \measuredangle1=\measuredangle4=\measuredangle2, \\ \measuredangle3=39^(\circ), \\ \measuredangle1+39^(\circ)=90^(\circ). \end{gathered}`

Solving the last equation for angle 1 we get:

`\begin{gathered} \measuredangle1=90^(\circ)-39^(\circ), \\ \measuredangle1=51^(\circ). \end{gathered}`

Answer:

`\begin{gathered} m\angle1=51^(\circ), \\ m\angle2=51^(\circ), \\ m\angle3=39^(\circ), \\ m\angle4=51^(\circ). \end{gathered}`