Question

find ( mangle i ) in rhombus ( ghij ).

Explanation:

Step1: Use the property of rhombus (adjacent angles are supplementary)

In a rhombus, adjacent angles are supplementary. So, \(5z+(4z + 90^{\circ})=180^{\circ}\).

Step2: Solve the equation for \(z\)

Combine like - terms: \(5z+4z+90^{\circ}=180^{\circ}\), which gives \(9z+90^{\circ}=180^{\circ}\).
Subtract \(90^{\circ}\) from both sides: \(9z=180^{\circ}-90^{\circ}=90^{\circ}\).
Divide both sides by \(9\): \(z = 10^{\circ}\).

Step3: Find \(m\angle G\)

Substitute \(z = 10^{\circ}\) into the expression for \(\angle G\): \(m\angle G=5z\), so \(m\angle G=5\times10^{\circ}=50^{\circ}\).

Step4: Use the property of rhombus (opposite angles are equal)

In a rhombus, opposite angles are equal. \(\angle I\) and \(\angle G\) are opposite angles.

Answer:

\(50\)