Question

find m∠h in rhombus efgh. m∠h = °

Explanation:

Step1: Recall property of rhombus

In a rhombus, adjacent - angles are supplementary, so \(m\angle G+m\angle F = 180^{\circ}\).
We know that \(m\angle G=(2c + 36)^{\circ}\) and \(m\angle F = 10c^{\circ}\). Then the equation is \((2c + 36)+10c=180\).

Step2: Solve the equation for \(c\)

Combine like - terms: \(2c+10c+36 = 180\), which simplifies to \(12c+36 = 180\).
Subtract 36 from both sides: \(12c=180 - 36=144\).
Divide both sides by 12: \(c=\frac{144}{12}=12\).

Step3: Find \(m\angle G\)

Substitute \(c = 12\) into the expression for \(m\angle G\): \(m\angle G=2c + 36=2\times12+36=24 + 36=60^{\circ}\).

Step4: Find \(m\angle H\)

Since \(m\angle G\) and \(m\angle H\) are adjacent angles in a rhombus, \(m\angle G+m\angle H = 180^{\circ}\).
So \(m\angle H=180 - m\angle G\).
Substitute \(m\angle G = 60^{\circ}\) into the equation: \(m\angle H=180 - 60=120^{\circ}\).

Answer:

\(120\)