Algebra homework help

Question

Mr. N divided the octagon into eight congruent isosceles triangles. What are the measurements of the three angles in each isosceles triangle?

If you divide a decagon into ten congruent isosceles triangles, what are the measures of the three angles in the isosceles triangles?

Given any regular polygon with side (n) that can be divided into congruent is isosceles triangles, what is the rule for determining the vertex angles of the isosceles triangles?

Three different questions :p

Answer 1

So, there is a trick to these problems. The key to understand is that, because each of these shapes is a bunch of triangles joined together at the middle of the shape, the sum of the angles in the center of the shape is 360 degrees.

So, for the octagon example, angles near the center sum to 360, and there are 8 of them, so each isosceles triangle has one angle that is 360/8, or 45 degrees.

In an isoceles triangle, two angles are the same and the sum of the three angles are 180 degrees. So, 45+2a = 180, a = 67.5 degrees

So, the equation for determining the vertex angles of the isosceles triangles is to divide 360 by the number of triangles (or the number of sides of the large shape)