Question

find m∠e and m∠d in rhombus defg. e 2y f 5y - 16° d g m∠e = ° m∠d = °

Explanation:

Step1: Recall rhombus property

Adjacent angles of a rhombus are supplementary, so \(m\angle E+m\angle F = 180^{\circ}\).

Step2: Set up the equation

We have \(2y+(5y - 16)=180\).
Combining like - terms gives \(7y-16 = 180\).
Adding 16 to both sides: \(7y=180 + 16=196\).
Dividing both sides by 7: \(y=\frac{196}{7}=28\).

Step3: Find \(m\angle E\)

Substitute \(y = 28\) into the expression for \(m\angle E\). Since \(m\angle E=2y\), then \(m\angle E=2\times28 = 56^{\circ}\).

Step4: Find \(m\angle D\)

Since \(m\angle D\) and \(m\angle E\) are adjacent angles in a rhombus, \(m\angle D + m\angle E=180^{\circ}\).
So \(m\angle D=180 - m\angle E\).
Substituting \(m\angle E = 56^{\circ}\), we get \(m\angle D=180 - 56=124^{\circ}\).

Answer:

\(m\angle E = 56^{\circ}\)
\(m\angle D = 124^{\circ}\)