Question

figure abcd is a parallelogram. what is the value of n? (2n + 32)° (4n - 2)°

Explanation:

Step1: Use property of parallelogram

In a parallelogram, consecutive angles are supplementary. But also, \(\angle B+\angle D = 180^{\circ}\) (adjacent angles in a parallelogram are supplementary). Wait, no, actually, in a parallelogram \(AB\parallel CD\), so \(\angle B+\angle C= 180^{\circ}\) and \(\angle A+\angle D = 180^{\circ}\), but another property: \(\angle B+\angle D=180^{\circ}\) (no, wrong). Wait, correct property: In parallelogram \(ABCD\), \(\angle B+\angle D = 180^{\circ}\) (adjacent angles are supplementary). Given \(\angle B=(2n + 32)^{\circ}\) and \(\angle D=(4n-2)^{\circ}\). Then \((2n + 32)+(4n-2)=180\).

Step2: Simplify the equation

Combine like - terms: \(2n+4n+32 - 2=180\), so \(6n+30 = 180\).

Step3: Solve for \(n\)

Subtract 30 from both sides: \(6n=180 - 30=150\). Then divide both sides by 6: \(n=\frac{150}{6}=25\).

Answer:

\(25\)