Question

Two parallel lines are cut by a transversal as shown below. Suppose m<6=102 degrees. Find m< 1 and m< 4.

Answer 1

m∠1=78°

m∠4=102°

Explanation:

Given: m∠6=102°

In the figure, angles 6 and 4 form an extended Z-shape. Thus, angles 6 and 4 are alternate angles.

Since alternate angles are equal in measure:

`\begin{gathered} m\angle4=m\angle6 \\ \implies m\angle4=102\degree \end{gathered}`

Next, angles 4 and 1 are on a straight line, therefore:

`\begin{gathered} m\angle4+m\angle1=180\degree \\ \implies102\degree+m\angle1=180\degree \\ m\angle1=180\degree-102\degree \\ m\angle1=78\degree \end{gathered}`

The measures of angles 1 and 4 are 78 degrees and 102 degrees respectively.