Question

yolanda is making a banner for a school pep rally. she cuts fabric in the shape of a parallelogram. the angle at the bottom - left corner measures 80°. what is the value of x?
options: 40, 50, 100, 160

Explanation:

Step1: Recall parallelogram angle property

In a parallelogram, consecutive angles are supplementary (sum to \(180^\circ\)), and opposite angles are equal. Here, the given angle (\(80^\circ\)) and \(x\) are consecutive? Wait, no—wait, looking at the diagram (parallelogram), adjacent angles? Wait, no, actually, in a parallelogram, consecutive angles (adjacent) are supplementary. Wait, but maybe the given \(80^\circ\) and \(x\) are same - side? Wait, no, let's think again. Wait, the bottom - left corner is \(80^\circ\), and the angle \(x\) is adjacent? Wait, no, in a parallelogram, consecutive angles (adjacent) are supplementary. Wait, no, actually, opposite angles are equal, and consecutive angles are supplementary. Wait, maybe the \(80^\circ\) and \(x\) are consecutive? Wait, no, let's check the options. Wait, the sum of consecutive angles in a parallelogram is \(180^\circ\). Wait, if one angle is \(80^\circ\), then the consecutive angle is \(180 - 80=100^\circ\)? Wait, but the options have 100. Wait, let's confirm.

In a parallelogram, \(\angle A+\angle B = 180^\circ\) (consecutive angles). So if one angle is \(80^\circ\), the consecutive angle \(x = 180 - 80=100^\circ\).

Step2: Calculate \(x\)

Using the property of parallelogram: consecutive angles are supplementary. So \(x=180 - 80\)
\(x = 100\)

Answer:

100 (corresponding to the option with 100, e.g., if the options are 40, 50, 100, 160, then the answer is the option with 100, like "100 (the option with 100 as its value)")