Question

find the measure of the three missing angles in the parallelogram below.
(there is a parallelogram image with angles labeled: top - left angle is ( x^circ ), top - right angle is ( 124^circ ), bottom - left angle is ( y^circ ), bottom - right angle is ( z^circ ))
answer attempt 1 out of 2
( x = square ) ( y = square ) ( z = square )

Explanation:

Step1: Recall properties of parallelograms

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

Step2: Find \(x\)

The angle \(x\) is opposite to \(z\), and consecutive to \(124^\circ\). So \(x + 124^\circ= 180^\circ\). Solving for \(x\): \(x = 180 - 124 = 56^\circ\).

Step3: Find \(y\)

Angle \(y\) is opposite to \(124^\circ\), so by opposite angles property, \(y = 124^\circ\).

Step4: Find \(z\)

Angle \(z\) is opposite to \(x\), so by opposite angles property, \(z = x = 56^\circ\).

Answer:

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