Question

grams
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, \((2n + 15)+(3n - 5)=180\).
Simplify the left - hand side: \(2n+15 + 3n-5=5n + 10\).
So, \(5n+10 = 180\).
Subtract 10 from both sides: \(5n=180 - 10=170\).
Divide both sides by 5: \(n=\frac{170}{5}=34\).

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

Substitute \(n = 34\) into \(\angle B=(2n + 15)^{\circ}\).
\(\angle B=(2\times34 + 15)^{\circ}=(68+15)^{\circ}=83^{\circ}\).

Step3: Use the property of parallelogram

In a parallelogram, \(\angle B+\angle D = 180^{\circ}\) (consecutive angles are supplementary).
So, \(\angle D=180^{\circ}-\angle B\).
Substitute \(\angle B = 83^{\circ}\), then \(\angle D=180 - 83=97^{\circ}\).

Answer:

\(\angle B = 83^{\circ};\angle D = 97^{\circ}\)