Question

figure abcd is a parallelogram. what are the measures of angles b and d? ∠b = 55°; ∠d = 55° ∠b = 55°; ∠d = 125° ∠b = 97°; ∠d = 97° ∠b = 83°; ∠d = 97° (2n + 15)° (3n - 5)°

Explanation:

Answer:

In a parallelogram, opposite - angles are equal. So \(\angle B=\angle D\).
Since \(\angle A\) and \(\angle D\) are adjacent angles in a parallelogram, \(\angle A+\angle D = 180^{\circ}\) (adjacent angles of a parallelogram are supplementary). Also, \(\angle A=(2n + 15)^{\circ}\) and \(\angle D=(3n-5)^{\circ}\). Then \((2n + 15)+(3n-5)=180\), \(5n+10 = 180\), \(5n=170\), \(n = 34\).
\(\angle D=(3n - 5)^{\circ}=(3\times34-5)^{\circ}=(102 - 5)^{\circ}=97^{\circ}\), \(\angle B=\angle D = 97^{\circ}\)
C. \(\angle B = 97^{\circ};\angle D = 97^{\circ}\)