Final answer:
The measure of angle M must be 70° to satisfy the triangle's angle sum property, but an equilateral triangle cannot be formed with the given angles.
Step-by-step explanation:
To prove that all sides of a triangle with angles N = 70°, M = 70°, and A = 40° are congruent, thereby making it an equilateral triangle, you need to ensure that all angles are equal. The only way to do this is if the measure of angle M (angle 7) is also 70°. By definition, an equilateral triangle has all sides equal in length, which necessitates that all interior angles are also equal, each being 60°. However, since the angles are given as N = 70° and A = 40°, which do not add up to 120° (the total required for two angles in an equilateral triangle), this triangle cannot have all sides congruent with the given angles. Additionally, the sum of angles in a triangle must equal 180°, so if angle N and angle A already sum up to 110°, the measure of angle M must be 70° to satisfy the triangle's angle sum property. So the correct answer to the question is A) 70°.