Question

select the correct answer from each drop - down menu. abcd is a parallelogram. m∠x = m∠y = m∠z =

Explanation:

Step1: Use property of parallelogram

In parallelogram \(ABCD\), \(\angle A=\angle C\). So \(m\angle x = 63^{\circ}\) since \(\angle C = 63^{\circ}\).

Step2: Use angle - sum in triangle

In \(\triangle ABD\), we know one angle is \(72^{\circ}\) and \(\angle A=63^{\circ}\). By the angle - sum property of a triangle (\(180^{\circ}\) in a triangle), \(m\angle y=180-(72 + 63)=45^{\circ}\).

Step3: Use property of parallelogram and angle - relationships

\(\angle ABD\) and \(\angle BDC\) are alternate interior angles. Since \(\angle ABD = 72^{\circ}\), \(m\angle z = 72^{\circ}\).

Answer:

\(m\angle x = 63^{\circ}\), \(m\angle y = 45^{\circ}\), \(m\angle z = 72^{\circ}\)