Question

find the measure of the three missing angles in the parallelogram below. answer attempt 1 out of 2 ( x=quad y=quad z= )

Explanation:

Step1: Recall properties of parallelograms

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

Step2: Find \(x\) and \(z\)

The angle given is \(124^\circ\). The angle \(x\) is opposite to \(z\)? Wait, no, in the parallelogram, consecutive angles: the angle \(x\) and \(124^\circ\) are consecutive? Wait, looking at the diagram, the angle \(x\) and \(124^\circ\) are consecutive? Wait, no, in a parallelogram, opposite angles are equal. Wait, the angle \(x\) and \(z\)? Wait, no, let's correct. In a parallelogram, opposite angles are equal, and consecutive angles are supplementary. So the angle adjacent to \(124^\circ\) (let's say \(x\)): \(x + 124^\circ= 180^\circ\), so \(x = 180 - 124 = 56^\circ\). Then, opposite angles: \(x = z\) (since they are opposite), and \(y = 124^\circ\) (since \(y\) is opposite to \(124^\circ\)). Wait, let's recheck. So consecutive angles: \(x\) and \(124^\circ\) are consecutive, so \(x = 180 - 124 = 56\). Then \(y\) is opposite to \(124^\circ\), so \(y = 124\). \(z\) is opposite to \(x\), so \(z = 56\).

Step3: Verify

Check: In a parallelogram, sum of all angles is \(360^\circ\). So \(124 + 124 + 56 + 56 = 360\). \(124*2 = 248\), \(56*2 = 112\), \(248 + 112 = 360\). Correct.

Answer:

\(x = 56\), \(y = 124\), \(z = 56\)