Main Answer:
An exterior angle at the base of an isosceles triangle is always
A. an obtuse angle
Therefore, the correct answer is A. an obtuse angle.
Step-by-step explanation:
In an isosceles triangle, two sides are of equal length, which means that the base angles opposite those sides are also equal. When an exterior angle is formed at the base, it becomes the sum of the two remote interior angles. Since one of the interior angles is acute and the other is obtuse, their sum, the exterior angle, is always obtuse. This is because the acute angle cannot compensate enough to make the sum a right or acute angle. Therefore, option A, "an obtuse angle," accurately describes the nature of the exterior angle in this context.
Understanding this geometric property is crucial in various mathematical and practical applications. It helps in solving problems related to angles in triangles and contributes to a broader understanding of geometry. The certainty of the obtuse nature of the exterior angle in an isosceles triangle is derived from the fixed relationship between the base angles and the exterior angle. In summary, the exterior angle's inevitability as obtuse is a fundamental aspect of isosceles triangles, providing a reliable rule for geometric analysis.
Therefore, the correct answer is A. an obtuse angle.