Final answer:
The angle between the base and altitude of an isosceles triangle with one exterior angle of 80° is 40°. This is determined by subtracting the exterior angle from 180° to find the adjacent interior angle and then solving for the base angles which are equal.
Step-by-step explanation:
Understanding the properties of triangles is essential in mathematics. In this case, we are given one exterior angle of an isosceles triangle which is 80°. The sum of the exterior angle and its corresponding interior angle is 180°. Therefore, the adjacent interior angle would be 180° - 80° = 100°. Since it is an isosceles triangle, the two base angles are equal, and the two angles that include the altitude are also equal. Let's call the base angle β. Hence, we have 2β + 100° = 180° (sum of angles in a triangle), which leads to 2β = 80°, and therefore β = 40°.
The angle between the base and altitude is the same as the base angle, which in an isosceles triangle is also the same as the angle at the apex halved. Therefore, the angle between the base and the altitude in this case is 40°.