Question

find the value of a in the parallelogram.

( a=square ) (simplify your answer.)

Explanation:

Step1: Use the property of parallelogram

In a parallelogram, consecutive angles are supplementary. But here, we can also use the property that in a parallelogram, opposite angles are equal. Wait, no, actually, for adjacent angles in a parallelogram, they are supplementary. Wait, no, hold on, the given angles \((5a - 4)^{\circ}\) and \((3a+30)^{\circ}\) are consecutive angles. In a parallelogram, consecutive angles are supplementary, so \((5a - 4)+(3a + 30)=180\).

Step2: Simplify the equation

Combine like - terms: \(5a+3a-4 + 30=180\), which is \(8a+26 = 180\).

Step3: Solve for \(a\)

Subtract 26 from both sides: \(8a=180 - 26\), so \(8a=154\). Then divide both sides by 8: \(a=\frac{154}{8}=\frac{77}{4}=19.25\).

Answer:

\(a = 19.25\)