Question

find the measure of the three missing angles in the parallelogram below.
image of a parallelogram with one angle labeled 82°, and the other three angles labeled x°, y°, z° respectively

Explanation:

Step1: Recall properties of parallelograms

In a parallelogram, opposite angles are equal, and consecutive angles are supplementary (sum to \(180^\circ\)).

Step2: Find angle \(x\)

Angle \(x\) is consecutive to the \(82^\circ\) angle. So, \(x + 82^\circ= 180^\circ\). Solving for \(x\), we get \(x = 180^\circ - 82^\circ= 98^\circ\).

Step3: Find angle \(y\)

Angle \(y\) is opposite to the \(82^\circ\) angle. By the property of parallelograms (opposite angles are equal), \(y = 82^\circ\).

Step4: Find angle \(z\)

Angle \(z\) is opposite to angle \(x\) (which is \(98^\circ\)). By the property of parallelograms (opposite angles are equal), \(z = x = 98^\circ\).

Answer:

The measures of the missing angles are \(x = 98^\circ\), \(y = 82^\circ\), and \(z = 98^\circ\).