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 property of parallelogram

In a parallelogram, consecutive - angles are supplementary (sum to 180°) and opposite - angles are equal.

Step2: Find angle B

Since ∠A and ∠B are consecutive angles in a parallelogram, and ∠A + ∠B=180°. Given ∠C = 116°, and ∠A = ∠C (opposite angles in a parallelogram), so ∠A = 116°. Then ∠B=180° - ∠A = 180° - 116°=64°.

Step3: Find angle D

Since ∠D and ∠C are consecutive angles in a parallelogram, ∠D + ∠C = 180°. So ∠D=180° - ∠C = 180° - 116° = 64°.

Answer:

64°