Question

find m∠d and m∠e in rhombus defg.

m∠d = \boxed{}^{\circ}
m∠e = \boxed{}^{\circ}

Explanation:

Step1: Recall rhombus angle property

In a rhombus, consecutive angles are supplementary (sum to \(180^\circ\)). So, \(m\angle D + m\angle E = 180^\circ\). Given \(m\angle D = 2v - 24^\circ\) and \(m\angle E = v\), we set up the equation:
\((2v - 24) + v = 180\)

Step2: Solve for \(v\)

Combine like terms:
\(3v - 24 = 180\)
Add 24 to both sides:
\(3v = 180 + 24 = 204\)
Divide by 3:
\(v = \frac{204}{3} = 68\)

Step3: Find \(m\angle D\) and \(m\angle E\)

For \(m\angle E\): Substitute \(v = 68\) into \(m\angle E = v\), so \(m\angle E = 68^\circ\).
For \(m\angle D\): Substitute \(v = 68\) into \(m\angle D = 2v - 24\):
\(m\angle D = 2(68) - 24 = 136 - 24 = 112^\circ\)

Answer:

\(m\angle D = 112^\circ\), \(m\angle E = 68^\circ\)