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=57-5

4x=57-5\implies 4x=52\implies x=\frac{52}{4}\implies x=13

The required value of x is:

x=13

**Similar post**

2. The base of a triangle is decreasing at a rate of 13 millimeters per minute.

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