Step-by-step solution-:
Given:
In rhombus FGHI
m\angle{HIJ}=57^{\circ}, m\angle{FIJ}=(4x+5)^{\circ}By using Rhombus Opposite Angles Theorem
If a parallelogram is also a rhombus, then its diagonal is an angle bisector for a pair of opposite angles.
We can say that:
\textcolor{primary}{m\angle{HIJ}} \textcolor{secondary}{=m\angle{FIJ}}Substitute the value of
\textcolor{primary}{m\angle{HIJ}}\textcolor{primary}{=57^{\circ}},\textcolor{secondary}{m\angle{FIJ}=(4x+5)^{\circ}}into the above expression:
\textcolor{primary}{57^{\circ}}=\textcolor{secondary}{(4x+5)^{\circ}}\implies 4x=57-54x=57-5\implies 4x=52\implies x=\frac{52}{4}\implies x=13The required value of x is:
x=13
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