Question

1. in the space below, use a straightedge to draw two intersecting lines. make sure the lines are not perpendicular.
2. measure each of the four angles you created with your protractor. write the angle measures in your picture.
3. what do you notice about angles that are across from each other?
4. what do you notice about angles that are next to each other?
5. lets see if these patterns hold. write your angle measurements in our class chart.
6. what conjectures can you make after seeing the class data?
7. why do you think this works? come up with a convincing argument.
8. without using a protractor, find the measures of x, y, and z.

x =____ y =__ z =____

Explanation:

Step1: Recall vertical - angle property

Vertical angles are equal. The angle opposite the 38° angle is also 38°.

Step2: Recall linear - pair property

A linear pair of angles sums to 180°. For the angle \(x\) and the 38° angle which form a linear pair, \(x = 180 - 38=142^{\circ}\).

Step3: Use vertical - angle property again

The angle \(y\) is vertical to \(x\), so \(y = 142^{\circ}\). The angle \(z\) is vertical to the 38° angle, so \(z = 38^{\circ}\).

Answer:

\(x = 142^{\circ}\), \(y = 142^{\circ}\), \(z = 38^{\circ}\)