The only possible measures for the two remote interior angles of the triangle are 20° and 80°. The correct answer is option B.
The sum of the remote interior angles of any triangle is always equal to the measure of the exterior angle that is not adjacent to it. In this case, the exterior angle measures 100°.
To find the possible measures of the two remote interior angles, we subtract the measure of the exterior angle from 180° (the sum of the interior angles of a triangle).
180° - 100° = 80°
So, the sum of the two remote interior angles is 80°.
Now, let's consider the options:
A. 40° and 60°: If we add these two angles together, we get 40° + 60° = 100°, which is not equal to the given exterior angle of 100°. Therefore, option A is not correct.
B. 20° and 80°: If we add these two angles together, we get 20° + 80° = 100°, which is equal to the given exterior angle of 100°. Therefore, option B is correct.
C. 50° and 80°: If we add these two angles together, we get 50° + 80° = 130°, which is not equal to the given exterior angle of 100°. Therefore, option C is not correct.
D. 50° and 30°: If we add these two angles together, we get 50° + 30° = 80°, which is not equal to the given exterior angle of 100°. Therefore, option D is not correct.
Based on the calculations, the only possible measures for the two remote interior angles of the triangle are 20° and 80°, which is option B.
The probable complete question could be
An exterior angle of an isosceles triangle measures 100°. Which could be the possible measures of the two remote interior angles of the triangle? A 40° and 60° B. 20° and 80° C. 50° and 80° D. 50° and 30°