Question

find the measure of the three missing angles in the parallelogram below.

answer attempt 2 out of 2
x =
y =
z =
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Explanation:

Step1: Recall properties of parallelogram

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 \(z\), and consecutive to \(124^\circ\). So, \(x + 124^\circ= 180^\circ\), thus \(x = 180 - 124 = 56^\circ\). Since opposite angles in a parallelogram are equal, \(z = x = 56^\circ\).

Step3: Find \(y\)

Opposite angles in a parallelogram are equal, so \(y\) is opposite to \(124^\circ\), hence \(y = 124^\circ\).

Answer:

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