Question

Maya designed two intersecting roads. She drew the roads so that one of the angles at the intersection was 45 degrees. What are the three other angle measures formed by the intersection? Draw a picture and explain your answer.

Answer 1

The sum of opposite angles are equal, so two of the angles are 45°.  The sum of all angles about the intersection of two lines is 360°.  So the remaining two angles are found by:

α=(360-2*45)/2

α=135°  thus all four angles are:

45°,135°,45°,135°