Question

using the supplementary consecutive angles theorem
manuela is making a banner for a school dance. she makes one angle 116°. what should she make the measures of angles b and d so that the banner is a parallelogram?
64°
116°
128°
244°

Explanation:

Step1: Recall the property of consecutive angles in a parallelogram

In a parallelogram, consecutive angles are supplementary. That is, the sum of consecutive angles is \(180^{\circ}\).

Step2: Calculate the measure of angle \(B\)

Since \(\angle A\) and \(\angle C\) are not consecutive (but \(\angle B\) and \(\angle C\) are consecutive). Let's use the property. If we consider \(\angle A\) and \(\angle D\) (assuming the figure is a parallelogram \(ABCD\) with \(AB\parallel CD\) and \(AD\parallel BC\)). Wait, no, for consecutive angles: \(\angle B\) and \(\angle C\) are consecutive. \(\angle B + \angle C=180^{\circ}\). Given \(\angle C = 116^{\circ}\), then \(\angle B=180^{\circ}-\angle C\).

$$ \angle B=180 - 116=64^{\circ} $$

In a parallelogram, opposite angles are equal. \(\angle B=\angle D\) (because \(AB\parallel CD\) and \(AD\parallel BC\), by the properties of parallelograms: opposite angles are congruent). So \(\angle D = 64^{\circ}\)

Answer:

\(64^{\circ}\)