Question

find the measure of the three missing angles in the parallelogram below.
answer
x = 75 y = 105 z = 105

Explanation:

Step1: Recall properties of parallelograms

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

Step2: Find \(x\)

Since opposite angles in a parallelogram are equal, the angle opposite to \(75^\circ\) is \(x\). So \(x = 75^\circ\) (opposite angles of parallelogram are equal).

Step3: Find \(y\)

Consecutive angles in a parallelogram are supplementary. So \(y + 75^\circ= 180^\circ\). Solving for \(y\), we get \(y = 180^\circ - 75^\circ = 105^\circ\).

Step4: Find \(z\) (assuming \(z\) is the angle opposite to \(y\))

Since opposite angles in a parallelogram are equal, the angle opposite to \(y\) (which is \(z\)) is equal to \(y\). So \(z = y = 105^\circ\).

Answer:

\(x = 75^\circ\), \(y = 105^\circ\), \(z = 105^\circ\)