Weare given a regular figure, and asked for the measure of some indicated angles as shown below:
Notice that this is regolar figure (all sides of the same size) and also that is has 8 sides. Therefore, the central angle (360 degrees) must be divided by 8 to find the measure of angle <1:
angle <1 = 360 / 8 = 45 degrees.
Now, since the little triangles that the polygon is divided into, are all isosceles triangles (have the two sides connected to the center of the polygon, equal, then the other two angles inside each triangle must be equal (let's call them "x").
Now, for each little triangle we use the property that the addition of its internal angles must equal 180 degrees:
<1 + x + x = 180
45 + 2 x = 180
2 x = 180 - 45
2 x = 135
x = 67.5 degrees
Then <1 = 45 degrees , and <2 = 67.5 degrees.