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?
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°
