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°

Explanation:

Step1: Use property of parallelogram

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

Step2: Solve for \(n\)

Simplify the equation: \(2n+15 + 3n-5=180\), which becomes \(5n+10 = 180\). Subtract 10 from both sides: \(5n=170\). Divide by 5: \(n = 34\).

Step3: Find \(\angle B\)

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

Step4: Find \(\angle D\)

Substitute \(n = 34\) into \(\angle D=(3n - 5)^{\circ}\). So, \(\angle D=(3\times34 - 5)^{\circ}=(102 - 5)^{\circ}=97^{\circ}\).

Answer:

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