Reference Angles, The Bow Tie Problem

Mike Day
Making sense of reference angles! As you can see, the 4 quadrants have the same triangles, thus making a bow tie. Grab and move point D in the first quadrant to change the angles. Click on the box marked Angles to show all the angles that have reference to the angle in the first quadrant. Click on the box marked Congruent Polygons to show the 4 triangles. Click on the boxes with Angles and see the actual angles. Notice the points that are shown and their values. Make sure to note the signs of each x-value and y-value.
You are starting with an angle of 43 degrees. What would the other three angles in each quadrant be? Change the original angle to 58 degrees. Find the reference angle in each quadrant.