Question

Find the value of p that makes the figure a parallelogram. Show your steps. (b) Find the value of q that makes the figure a parallelogram. Show your steps.

Answer 1

Aparallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

So, the opposite angles are equal we have,

$\begin{gathered} p+100=13q+4 \\ 9q=72 \end{gathered}$

On solving , we have,

$9q=72\rightarrow q=\frac{72}{9}=8$

Thus, q = 8. Substituting this value in the first equation, we have,

$\begin{gathered} p+100=13\times8+4 \\ p+100=108 \\ p=108-100=8 \end{gathered}$

Thus, p = q = 8.