Question

find the value of each variable in the parallelogram. the figure is not drawn to scale. a = t = k = (type whole numbers)

Explanation:

Step1: Find the value of \(a\)

In a parallelogram, opposite sides are equal. So, \(a + 19=33\).
Subtract 19 from both sides: \(a=33 - 19\).
\(a = 14\).

Step2: Find the value of \(t\)

In a parallelogram, consecutive angles are supplementary. So, \(3t+9t = 180\).
Combine like - terms: \(12t=180\).
Divide both sides by 12: \(t=\frac{180}{12}\).
\(t = 15\).

Step3: Find the value of \(k\)

In a parallelogram, \(k = 9t\) (opposite angles are equal).
Since \(t = 15\), then \(k=9\times15\).
\(k = 135\).

Answer:

\(a = 14\), \(t = 15\), \(k = 135\)