Question

Bill draws a regular octagon. He divides the octagon into eight congruent isosceles triangles. What are the measures of the three angles in the isosceles triangle?

Answer 1

See the picture attached to better understand the problem

we know that
the formula for calculate the sum of the internal angles in a regular polygon is
Sum=(n-2)*180
for n=8
sum=(8-2)*180----> 1080°
1080°----> divide by number of sides
1080/8=135°
so
in the figure
∠ BAD=135°
∠ BAC=∠ BAD/2---> 135°/2---> 67.5°
∠ BAC=67.5°

the triangle ABC is an isosceles triangle
so
∠ ABC=∠ BAC
∠ ABC=67.5°
the sum of the internal angles of the triangle is equal to 180 degrees
∠ BCA=180-(67.5+67.5)------> 45°
∠ BCA=45°

the measures of the three angles in the isosceles triangle are
∠ BAC=67.5°
∠ ABC=67.5°
∠ BCA=45°