Final answer:
The ratio of the vertex angle to a base angle of an isosceles triangle with a base angle of 70° is 4:7.
Step-by-step explanation:
To find the ratio of the vertex angle to a base angle of an isosceles triangle when a base angle is 70°, we first need to understand that an isosceles triangle has two equal sides and two equal angles. Since the sum of angles in any triangle is 180°, we can calculate the vertex angle. With one base angle being 70°, the other base angle is also 70°, which means the vertex angle must be 180° - 70° - 70° = 40°. Now, we can form the ratio of the vertex angle to a base angle, which is 40° : 70° or simplifying it, 4 : 7.