Question

Select the correct choices to complete the sentence.

ANALYZE In △ABC,if an exterior angle adjacent to ∠A is acute, is the triangle acute, right, or obtuse, or can its classification not be determined? Explain your reasoning.

Answer 1

The triangle is obtuse, because the exterior angle is acute, the sum of remote interior angles must be acute, which means that the third angle must be obtuse. Therefore, the triangle must be obtuse.

What is an obtuse triangle?

An obtuse triangle is a type of triangle in which one of its angles measures more than 90 degrees.

Given that in △ABC, the exterior angle adjacent to angle A is acute, it means the measure is less than 90 degrees.

Therefore, the measure of angle A = an angle measure that must be greater than 90 degrees.

Since angle A is greater than 90 degrees, then △ABC can be classified as an obtuse triangle.