Question

Find the values of variables x,y and z in the parallelogram

Answer 1

Given a parallelogram,

Opposite sides of a parallelogram are parallel

The parallelogram have being bisected into two equal triangles

`\begin{gathered} y\degree+33\degree+109\degree=180\degree\text{ (sum of angles in a triangle)} \\ y\degree+142\degree=180\degree \\ \text{Collect like terms} \\ y\degree=180\degree-142\degree \\ y\degree=38\degree \end{gathered}`
`x\degree=33\degree(alternate\text{ interior angles)}`
`z\degree=109\degree\text{ (opposite angles of a parallelogram are equal)}`

Hence, the answers are

`\begin{gathered} x\degree=33\degree \\ y\degree=38\degree \\ z\degree=109\degree \end{gathered}`