The ratio of the measure of a base angle in an isosceles triangle to the measure of the vertex angle is 1: 7

Assuming you require the measure of the angles

let x represent each equal  base angle then vertex = 7x

The sum of the angles in a triangle = 180°, hence

x + x + 7x = 180

9x = 180 ( divide both sides by 9 )

x = 20

the base angles = 20° and the vertex = 140°

828. all there is to it!

here, if you ever need with rounding (or other forms of arithmetic/math) again, use this:

thats the rounding one, but if you just click the top left, it shows you all the calculators you may need!

this doesn't make sense lol