Question

parallelograms
figure abcd is a parallelogram
what are the measures of angles b and d?

Explanation:

Step1: Use the property of parallelogram

In a parallelogram, consecutive angles are supplementary. So, \((2n + 15)+(3n - 5)=180\)

Step2: Solve the equation for \(n\)

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Step3: Find the measure of \(\angle B\)

Substitute \(n = 34\) into \(\angle B=(2n + 15)^{\circ}\), \(\angle B=(2\times34 + 15)^{\circ}=(68+15)^{\circ}=97^{\circ}\)

Step4: Use the property of parallelogram (opposite angles are equal)

In a parallelogram, \(\angle B=\angle D\) (opposite angles of a parallelogram are equal). So \(\angle D = 97^{\circ}\)

Answer:

\(\angle B = 97^{\circ}\); \(\angle D = 97^{\circ}\) (corresponds to the option \(\angle B = 97^{\circ}\); \(\angle D = 97^{\circ}\))