Question

a parallelogram has one angle that measures 112°. what are the measures of the other three angles in the parallelogram?
□°, □°, and □°
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Explanation:

Step1: Recall parallelogram angle properties

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

Step2: Find the measure of the angle opposite to \(112^\circ\)

Since opposite angles in a parallelogram are equal, the angle opposite to \(112^\circ\) is also \(112^\circ\).

Step3: Find the measure of the consecutive angles

Let the measure of a consecutive angle be \(x\). Then, using the supplementary property, \(112^\circ + x = 180^\circ\). Solving for \(x\), we get \(x = 180^\circ - 112^\circ = 68^\circ\).

Step4: Determine the remaining angle

The angle opposite to this \(68^\circ\) angle is also \(68^\circ\) (because opposite angles in a parallelogram are equal).

Answer:

\(68\), \(112\), and \(68\)