The vertex angle of an isoceles triangle is 8 times the measure of the base angle. find the measure of the base angle

For this problem, if we used b to represent your base angle measurement, you would add 8b+2b and set it equal to 180. This is because the measure of the vertex angle is 8 times the base angle measurement, so we had to multiply b by 8. We also had to add it to the other angle measures, so the other angle measures are represented as 2b since they are the same length. We then have to set this equal to 180 since that measures of a triangle must add up to 180. Then we combine like terms on our "b" side to get 10b=180. Then we divide both sides by 10 and we get b=18, which is the measure of our base angle.