The vertex angle of an isosceles triangle is 40 degrees less than the sum of the measures of the base angles. Determine the measure of the vertex angle.
Let the base angles be x as both are equal in a isosceles triangle Now, x+x+(x-40)=180. Since sum of angles of a triangle 2x+(2x-40)=180 2x+2x-40=180 4x=180+40 4x=220 x=220/4 x=55
Now,they asked us vertex angle which is 40 degrees less than sum of base angles Therefore x+x-40=vertex angle 2x-40=vertex angle 2(55)-40=vertex angle 110-40=vertex angle Vertex angle =70 degrees
